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In Western society, it is very common for a teen to be moving out of their homes at the age of say around 17, 18 or 19 after they have graduated high school and moving on to college or university. Especially if the school that they have admitted to and planning to go to is very far from where they live, it would be better to find a place – may it be a residence, own room, a dormitory, or a condo near the school. That’s a great work around for commuting far or driving long distance just to get to school from home right? And another good thing about it is that you get some good sense of freedom there, doing whatever you want. No one to boss you – well, not really cause the landlord would most likely be banging on your door the same day every month collecting rent. Anyway, my point is you will be “free” if you know what I mean from whatever hell you just go through with siblings or parents or any family member – unless if you will be actually staying with another sibling or relative or family member when you move out, then there’s still that problem there. But like I said this is a Western society.
In my world, the Asian Filipino world. Doesn’t matter whether I’m the Western side or I’m in my side, family always comes first. I live in a culture where families are bound together, doing whatever they can not be separated. They would not want a single one to be isolated or left behind. So they would always live together. Even if age doesn’t dictate moving out unlike for the Westerners, we would still live together. But does that mean that I like it? Does that mean we like it? For some people, this is the way of life. It has to be this way. Very traditional and conservative. Others would like to deviate from this notion and be “free”. I’m one of them. So I guess you could say that I was being forced to remain in the nest even though I have reason to believe to be “free”.
Another reason why I’m still here under their roof is that my school is just closeby. Just 30 minutes by bus local and 20 minutes by bus express, 45 minutes to an hour by bus on rush hours. Not too bad. Was hoping I could drive but have no car and can’t lol. I promise a story on this next time. So getting my own place wouldn’t be necessary, and also getting my own place is just expensive.
So there you have it. Three reasons why I’m still here, (1) strict family ties by culture, (2) nearby school, and (3) expensive place. Hopefully someday I would be able to get my own place. I just really wanted to. It will be a great way to learn things on my own, be independent, and most importantly take action and responsibility for any decision that I may have made – you know, know and understand the consequences of my actions. But for now, I guess I’ll just be here…
Hello to you! Welcome to my blog, and if you’re new here – please follow me up. Now I sounded like a Youtuber there, lol. Anyways, for this blog post I’d like to share my experience relating to love and relationships. But trust me, it’s never “a” love. And it’s also never “a” relationship. I wish I could tell the context of when this happened, but I don’t think I can since the person involved is a friend of mine that happens to follow me here. Furthermore, I would hide her true identity and let’s just call her Jenny.
So Jenny is quite a lovely nice girl. And by that I mean that she is very reserved and conservative, well that’s how I at least remember her. She is 5 feet 8 or 9 inches. I think she’s as tall as I am, or if not then maybe shorter. She has a black straight hair, with a pinkish frecklish face but the freckles didn’t matter. She had a nice smile that she always puts on her face. Background nationality, she’s Asian. And that’s really nice too because I have always had a thing for Asians, just like me. So anyway, she would have been perfect.
Ok backtrack a bit. Where did I first meet her? We met back in high school. But back then she was quiet and shy. She was always alone and loner and had no friends. She would rather and prefer to be alone, isolating herself from the crowd. She didn’t join any clubs nor attend and participate in any school activities (except for those required ones like assemblies). She’s that type of person that goes straight home right after school. I would always notice her, but I don’t think she ever noticed me. She did attend prom, which quite surprised me. But apparently she was just there for the food, then left. Could it be that she didn’t like the food or perhaps threw up because of the horrible food they served? Or it’s just that prom isn’t her thing and don’t want to go hangin’ and dancing with other people. But anyway, she seemed that sweet, innocent girl. I liked those types of girls, and that’s why it’s always hard for me to be in a relationship – but anyway, that’s for another story.
So graduation came along. She was there for the graduation of course who wouldn’t. But then quickly disappeared after she got her diploma. I didn’t even get a chance to say goodbye to her. I mean she’s quite lovely, but I had my eyes set out for other/another girl(s) back then. I guess I like her kinda before? But just wasn’t sure.
Let’s fast forward along to university years. I went to York University, she went to University of Toronto (won’t say which campus, as to conceal identity as much as possible) for her first year. But when we became second year, I bumped into her at York. And we had a 5-10 minute conversation trying to catch up on each other. She said she was at University of Toronto but had to move to York because things are not working out (there’s just lots of reasons and I just can’t tell what they are because it would be too obvious now). So yeah, that’s what I learned about her. And she remembered me too! She matured a lot, and I mean a lot! And there was a whole change of her. She became more “talkative” in a sense that she was really quiet before, but she is still the same girl that’s very reserved, conservative, and likes to be in isolation. We part ways because I still had my class, and so did her too.
The next day, I saw her friend request on Facebook and I did accept it. She then messaged me and asked if I was free sometime during the week. I asked her why was she asking me and said that she wanted to ask me out (obviously she wanted to ask me out but keeps on using “hangout” as term). Weirdly enough, I lost my “feelings” over her from high school and moved on when I got to York. And apparently, there was this girl from Computer Science (btw Jenny’s in a business program) that I had my eyes on for a long time already and no one was into her too. I’m becoming close with this girl so I wouldn’t want to let go of that opportunity; anyway, another story for that. So instead of making Jenny feel bad, I just made an alibi saying I can’t as I have midterms to study for. It all ended with the “maybe next time” message. But trust me, I was getting a lot of these messages from her for next 3-4 semesters or so, not on a weekly basis but on an occasional basis. It’s quite getting creepy and “stalking” feeling but not really. It’s just that she is no longer my type, I don’t think I would want her really. And that she has to take a hint and just move on.
Ok moving on to a few more months. I bought two tickets to see a superhero Marvel movie, one for myself and one for a friend that wanted to see the movie with me. Chill, it’s not Jenny but some other guy dude friend. Anyway, he’s not important because the day after I bought those non-refundable tickets, my friend that I was supposed to go watch the movie with ditched me and said that he can’t make it as his girlfriend had just got him tickets as well but for another movie. Damn, of course my friend would have to pick his girl even if it wasn’t the Marvel movie that we were psyched about to watch. So now, I have no choice but literally look for someone to watch me. Damn. There was just no one. It was hard looking for someone to watch with me because people were either busy, the time wasn’t convenient enough, people already made plans or it was too last minute. But then for some reason, I thought of Jenny. She always wanted to go (hang)out with me. So I messaged her and asked her if she’s free on the Friday of the movie and if she wanted to see the show. She said yes, which is good in my part because I wouldn’t worry about a wasted ticket. But also not good because that wasn’t intentional and I just wanted to get someone so that the ticket won’t get wasted. I didn’t charge her for the ticket anymore, that just shows shittiness on the part of me as a guy, since I did ask her out.
We then met each other in the movie theatre and she bought us popcorn. Well that’s good, I got the tickets and she got popcorn. Hooray! We met up half an hour before the movie and we talked and tried catching up. She was more mature like I said and “prettier” too. I kinda liked her. I had that daydreaming imaginary thought of “What if I fall for her and we become together?” I’ve always had that theory that she likes me just because of how her gestures and body language are when facing me in person, and that she always tries asking me out and I always say no. Lol. But that theory has to be confirmed somehow. This meetup/hangout/date or whatever you call it, will have had confirmed it. So movie starts. Movie ends. Then we went to the foodcourt for dinner. Fine dining was just not the option for her because she said it was too fancy. And I kinda gotten the hint that she was actually not into me because I always think that a girl is more likely to be into you if you dine on in a fancy resto. Well, that’s just theory again. I also got another hint of her not liking me after we saw the movie. She doesn’t seem to be too excited after. I just thought she got bored of it. I even asked her before the movie if she likes movies (she said yes). I asked her if she watched the movie trailer (she said no). I mean why did she not do her research, right? Is she not interested in the movie? The movie’s main character is a female persona. I do not know why she did not enjoy it. Another flag that I caught was when she asked me “Why did you ask me? Is it because XXX isn’t free?”, where XXX is the name of the girl that I usually hangout with from high school and continue to get a touch base until now occassionally. So Jenny’s like implying that she is only a second option, and laughed it out after. But I said no and told Jenny that I try to hangout with different people as much as possible. And holy wow, safe call for me. Dinner wasn’t as good as well. We ended up getting different foods from different restaurants in the food court. I got sushi, and she got salad/pizza. She only ate the salad lol. And brought the pizza home. She even offered half the pizza slice but I insisted not to since she paid for it. We were also talking during dinner and we talked a lot of commonalities between us, which is good, like Netflix shows that we watch. But then we also got a talk about some guys that tried hitting up on her at York. There was one guy she mentioned that she said that he was worried on our meetup/hangout/date, but apparently Jenny wasn’t interested at all at this guy. This guy even made a bet that the guy that Jenny will be going out with (me) literally has plans on dating her (well, I guess no at first because she was more of “I need someone to fill in an empty seat” but then yeah maybe after seeing her again). And I just said nah, and literally laughed it out. Cause now, I think I might have debunked my own theory of her liking me. It doesn’t seem like she’s interested in me after all, or into dating me or just dating anyone in general. She seemed like she was just wanting to be friends with me. She was still that reserved, conservative kind of person – very innocent too. And then she said that that guy owes her money now. Lol.
I was a gentleman still and we went home together, or at least brought her to the subway, took it and walked her to the bus stop. I just don’t know if she ever had feelings (or at least little) for me before and just moved on eventually getting a hint that I was not into her. Or did she actually never had feelings for me and just interested as a friend. I mean there is that “sense of rejection” there, now that I think about it. But it’s something I could easily deal with and just move on. I have no regrets and at least I enjoyed spending my time with Jenny. It was then there that I shouldn’t really force my self into her, or force my attraction or liking or feelings for her. Cause it just wouldn’t work. I know for a fact that I don’t really like her. Everything there seemed was just like “forcing”. It’s not genuine. It’s hard to not be genuine, especially in the long run. So I guess better than hurting feelings in the future where damage is already big, get them out of the way as early possible.
Welp, that ends my story about Jenny and I. I wouldn’t think of hanging out with Jenny again. If she asks me out or whatever, then I’ll try maybe? But if not and is on the mode of being the one to expect, then that’s not gonna happen. I’m on my “move on” status so yeah.
There’s a prequel story of how all these things came to be, and I had left them out – until I am ready to tell the story. But it will be a nice, juicy one which I promise to write about in the future. For now, don’t ever force yourself into love.
Yes I said it. And this is not a statement to down myself or to put my self-esteem down (nor to create a way to humble myself down, putting myself out there where I just show the opposite, and thus creating a drama or tea). All I am saying is that this sentence is true and it is something that I don’t think will change. I am not a writer nor a real author. It’s not a passion that I am proud of. I just would like to write, and that’s it. I want to express myself, putting down thoughts into words. So if you would realize and recognize that my other past posts are sh*t af. They were not even proof-read nor have I given myself two seconds to read over and look it. There are several spelling and grammar mistakes, modifiers misplaced and dangling, punctuations out of place, arguments unorganized. It’s literally gross and disgusting. But I chose to write anyway, and I chose to write, type it up and put it up. Whatever just comes to mind, I write it down. So I guess you can say that this is somehow my mind at work – really unorganized. And I do not wish to edit that because if I do, then the natural way of thinking has been modified. Cause what’s the point of proofreading and editing if I want to show how my brain works initially, how it demonstrates work.
But when are times that I do some changes? Well, it is something that my mind have an answer too but my mouth/tongue, fingers can’t even type. I don’t know why my mind “has a mind of its own”. So yeah you can call me “crazy” even but that’s alright. My mind IS weird. And writing something untouched is some style that I do not wish to change. This is my “brainstorming” expressed through text. I do not also use outlines; I only start typing the text up. But for those changes? I just don’t know.
So if you feel like my blog posts are sh*t, then there you go. That’s the reason and a future disclaimer. I’m not supposed to be posting today since I have put up a post yesterday called Why I Gave Up on Philosophy? and I only plan on blogging twice or three times a week. But I guess it’s alright since (1) that disclaimer needed to be put up sometime soon, and (2) I’m just bored as hell. I will also be updating my blog site; I’ve done a couple of updates so far as you have seen, more changes coming up by the end of the week until next week. ‘Til next post.
Back in the Philippines (before coming here), I have taken a Theology class which has inspired me (not about the gods or God for that matter; I’ll talk about religion some other time). An inspiration where I can channel my passions and interests in arts, culture, social media, entertainment, pop culture, etc. into something meaningful and articulative. In my Theology class, because I used to study in a Catholic school, then we had put our central faith in God (and yes with the capital ‘G’). So that’s what we had to do in our essays and papers. We incorporate and reference pop culture in our papers as the main style of the essays that we hand in. Analogies – from events to quotations from a song, music, movie, a play or anything really, would have to be used in order to explain and elaborate an argument that we are trying to persuade. I have never taken a Philosophy class before, but how we should be working on our Philosophy papers in the future should have a similar taste. Taking these Theology classes would prepare us for those higher levelled Philosophy classes where our central concentration tends to be in man. But anyway, those were the main heart core courses in my university in the Philippines and no one is graduating without taking 4 courses of Theology and 4 courses of Philosophy. So that’s what inspired me to pursue a major (or at least a minor in Philosophy). I enjoy the work that I do in Theology and if we will do the same in Philosophy, then I am sure in myself to enjoy it. Sure there were readings (and you know how I feel about readings, eck; but they were enriching and makes sense, but that’s for Theology side). I wasn’t able to take Philosophy back then but I’m pretty sure it will be similar.
Fast forward to 2014 when I came here to Canada from there. I “re-started” in high school (I can tell another story in another blog about this). So I decided that I wish to pursue a double major in Computer Science, then Mathematics, then do a minor in Philosophy. Back home in the Philippines, I was a CompSci student but unable to do a double major in Mathematics due to financial reasons. Here, when they allow me to double major in CompSci and Math, they did allow me: I first begin school as a CS major while taking 3 Math courses on my first semester, then begin my double major CS-Math major after that first semester. So now I’m doing my double major, which is good since they not only allowed me but does not provide extra costs to tuition fees. The electives I’m supposed to take as a CS student get replaced by Math courses as “electives”. So no additional fees are needed to paid; furthermore there is no need to take those general courses too since Math courses have already covered them for me.
Ok back to my dream of double majoring in CS and Math, then minoring in Philosophy. In high school as I said, I have thought of taking a Philosophy course in order to get a taste and get myself prepared of what I am about to face in Philosophy of university. There is the Grade 11 Philosophy, then there is the Grade 12 Philosophy course. The Grade 11 Philosophy only requires a Grade 10 English pre-requisite (but I need not the Grade 10 English pre-requisite as I have completed my ESL – English as Second Language courses). The Grade 12 Philosophy course needs a Grade 11 Philosophy (of course duh!) or a Grade 11 English for university. I had to take Grade 11 English for university first before taking the Grade 12 Philosophy (didn’t take anymore the Grade 11 Philosophy which I thought of “waste of time” lol); the Grade 11 English is also needed as a pre-requisite for Grade 12 English, which is required for any student who wishes to pursue university. So yeah. The Grade 12 English story needs another blog.
Anywho, so I took the Grade 12 Philosophy course – which I have to be honest I did not enjoy it. I will, in bullets, state reasons as to why I did not like it. It could be possible that the curriculum in our high school was not designed properly, the teacher could also be to blame, but to be honest it will just depend on luck and circumstance. To be honest the teacher was nice, I don’t blame her. It just did not come out right!
- The entire semester of Grade 12 Philosophy was nothing but readings. In our high school, classes run everyday. And each course runs everyday. Each course a student has is assigned with Period letters (A, B, C, D), with the time slots as follows: 9:00-10:15 AM, 10:20-11:35 AM, 12:35-1:50 PM, 1:55-3:10 PM. The morning time slots are either Period A or B, then the afternoon time slots are either Period C or D, depending on the date of the month. For an odd date, then it follows Period A, B, C, D. For an even date, periods switch up to B, A, D, C. So you would imagine that I will be attending that class every single day (Period A by the way), then same teacher. And it’s the morning too so every morning there is a new reading, and always asks us to answer questions on the book, take notes. There is always something new each day and we barely have time to cover everything. Most of the book was covered by self-studying in class every morning but she took less time to cover and discuss in class.
- There were different activities in class that just was ridiculous. The first one was we would pair up with someone else in class and perform a short Socratic dialogue in front of the class. It is usually Socrates and ____; my partner and I became Socrates and the fortune teller. He was Socrates, trust me plain. I was the fortune teller who had different sorts of props like a magic crystal ball (it’s only a small soccer ball covered in aluminum foil on top of a tape); also had fortune telling cards (not tarot cards but just a regular deck that I pre-dealt before the presentation started and was “pretending to read Socrates’ future/desitny/fate” through the cards but in fact, it only had keywords of what I was supposed to say so I wouldn’t forget them lol. We also did debates in class (we did a debate on whether a God exists or not; it’s ridiculous because you get assigned to a team and the teacher randomizes your side, which is ridiculous because I have my own faith and belief and you cannot make me change those beliefs by picking my side for me). We also worked on a couple of presentations (like I remember presenting the life of a philosopher named Friedrich Nietzsche). We also worked on small mini papers and one final paper. The small mini paper I remember involved watching one philosophical movie (I did “Ex Machina”) and writing a paper about it. I had expectations for it in terms of marks because I know I did well and exerted my best efforts into writing that paper only to find out I’m only getting an 86% for it (uggh!) For my final paper, I had to do a research paper (I literally went to different libraries in town, not just go to internet/Google/Wikipedia). It took me 3 weeks to complete the paper, and at least 4-5 times of visit to the library where I remember staying there until closing. I borrowed books to bring home; some cannot be brought home so I had to get some pages photocopied (I know taking a picture would have been better but just looked wrong lol). Anyway, the paper that I wrote was titled “The Good”, where in I argue the different takes and perspectives of what people think is “good” and what people think causes them to be happy? (What is “happiness” anyway?) I used different concepts from utilitarianism to Mill’s Theories to even virtue theories. And in conclusion, I give my own take of what I think is “good”, what makes something “good”, how is “happiness” defined and can be interpreted and can be incorporated into “good”. Trust me, it’s not an easy process and took a while. I enjoyed writing the paper. Again I was full-blast with this but wasn’t enough. Landed on an 89%. There were written tests too and the final exam. All just hard.
- I just think that the only reason why I started hating Philosophy and not liking it anymore was that I burning my ass out in reading, writing, and all my efforts drain away to something mid-80s. Like Idk why just why. The teacher is probably a reason too, she’s a tough marker. In the end, I ended with a flat 90. But it wasn’t as good as I wanted it to be. *sigh*
So this is where my decline for interest in pursuing a Philosophy minor begins. And now, I don’t want to experience the same thing that had happened to me. I do not want to touch Philosophy again and never will. Once of an experience was good; but if it’s an experience that didn’t go so well, then I just decided I’d rather not waste time and just move on. Hope it’s not just me out there that experience this (not just Philosophy but could be anything)…
So I just would like to get a touch-base on how I have been doing, what I have been doing, and other plans for the future. I can’t remember to be honest what was the context the last time I wrote here. I can’t remember what I have been up to. But all I know it was 2016. Three years later here I am. For this post, I just wish to give an update of how I am and plan for my future and what lies ahead. Also, I will little by little do some revelations of myself, which I have been concealing and hiding away out of fear from my past posts. But now I am free and am now wanting to show myself.
So anyway, I’m turning 23 in 2 months’ time (just do the maths for my current age, and my age in my last post here). I have started typing this 8:56 PM, sipping hot chocolate (’cause I don’t drink coffee); I’ll cook and eat dinner soon (perhaps as soon as I put this post up). I have just finished two years of undergraduate studies in a university. Currently doing a Computer Science and Math double major degree program. I’m now on my third year and currently out of school and doing my full-time internship as a data analyst in a business consulting company. I would like to share a lot of my experiences in my internship (perhaps next month, and I will do it on a March/June/August basis to give updates). The internship is 8 months long and I just started last month. I don’t intend on extending my internship contract nor look for other internship opportunities after completing this one. I would like to go back to school and finish my undergrad. My plan is still to go to graduate school, purse my master’s and my PhD – go to academia, be a professor and a researcher.
In terms of social life, I have been bringing a few closer, some far away. But I guess, that’s just how life goes. Things come and go. I will tell more about my social life soon. In terms of relationships and love life, I would like to tell a story about it some time soon as well. We’re currently facing something “undesirable” at the moment, and writing about our relationship right now might be affected if we still continue to have this issue. I will have to sort this out first before going to write about my love life. But everything will be explained in my blog post. In fact, due to the complication of things – I might split that into parts.
In terms of my jobs, I currently work full-time (Monday through Friday, 9-5 job; or sometimes 8:30-4:30). On Saturdays, I work part-time as a tutor. I have also recently began working freelancing over on Fiverr, I am currently just starting so I have almost nothing yet. But I would like it if someone buys my service and get the service need as soon as possible 😀 Well, idk how else to advertise, so here might help too 😀 (Please help me! 😀 ) Anyway, I offer LaTeX typesetting service, Math help, among others as my main most services. (I could talk more about Fiverr and freelancing in some future blogpost).
In terms of what my hobbies and pastimes, I am doing some side projects, namely on programming, coding and development. I plan on writing about these as well in the future. I could link you to some of my work. But these are all unfinished and are on ongoing continuous process (trust me, I have been very busy with school, holidays, internship, jobs and all that for the past few 8 months, so I am not very progressive on my work either but I still try). Here’s a mobile bank app I have been working on and the prime number game that have had no updates for like 2-3 years already lol (again due to time constraints). I’m also intrigued about other stuff like arts, history, museums, science, musics, dances, photography, and many more, thanks to my passionate S.O. (I’ll talk more about these soon). I’m also right now in the process of creating geek designs for tees. I plan on selling merch eventually, as soon as I get enough designs and get someone to get the production done – stay tuned for this one and I hope you will support me by purchasing my merch. And now blogging and cooking sessions came to be (I will write about those too!)
I remember in the past that I was writing a novel called The Isolation, and I was uploading here excerpts of the novel – some particular ones that I have already wrote. Two things: 1) I can’t find the files anymore, both here and in my local system. I had changed computers for the past years at least twice already! and I can’t remember where I have dumped them. It could be in my drives but I will have to still check; my flash drive is missing and can’t be found either! It’s not in WordPress either for some reason; I may have hidden them, idk. 2) I may decide to not continue writing the novel. It has been a long time ago, where my writing is very “dull”, and now is a bit “improved” I guess? So you’ll see a major gap change between before and after if I continue. I could proofread and review the old pages but again, I may not have time for those and it would be better to keep them as is and precious. Furthermore, going back to point 1 idk where are those files!
I have two titles that I plan on writing eventually, called Fire and Ice (or Fire and Water) and Dark Shadows. I have previously mentioned that in my previous blog. Nothing is final yet; I’m hoping they eventually get going. But Fire and Ice or Fire and Water would present, either literally or analogically or metaphorically, two entities that are not compatible and yet they are trying to be as one. I would have to draw based from my experience here in writing this title. I am still unsure if this is simply an essay, a short story, some fiction or a novel! Similar goes for Dark Shadows where I plan to talk about my darkness: negative thoughts, depression, bad experiences in life, etc. But again, I may not be the main character, but have someone else be and give him my “shadows”. If both titles would push through, this will be something amazing and an achievement indeed!
For now, I’m sticking blogs. I have future plans beyond the ones I have mentioned. YouTube could be one, but we’ll see. ‘Til next time.
Feels good to be back! It has been a while since my last post… Like literally, I opened this blog and the last time was in December 2016! Oh wow that was like 2 years ago, going to 3 by the end of the year. And my first blog post was in November of 2013, which was almost 5-6 years ago! But now I’m back, I am ready to return to my blog journey. I have been very busy about things over the years, but that doesn’t mean I am no longer busy now. I am wanting to engage myself in a hobby, in a pastime, or basically anything that would keep my mind off of my personal problems. I have a lot of stories to share and post. I know a lot of my old posts were stories, and a lot of them were even fictional! I was even reading them now and I am cringing the hell on my seat just reading them!
Anyways, from now on I will try to be consistent with my post schedule – twice or thrice a week. I cannot be certain of which days of the week, but I will be trying. A lot of things happened to me after all those years and I would like to talk to you about them here. Here’s a list of some things I have in mind to talk about (whether personal self, fiction stories, or anything under the sun):
- My schooling
- My work/internship
- My relationships/love life
- My life and adventures in Toronto
- Other things about me
- Computer Science and Math talks
- Fan fictions
- Anything about Youtube and Netflix
- Social media talks
- “Fire and Ice”
- “Dark Shadow”
These would be in no particular order. And I promise to put up at least three things this week. I would also be updating my entire WordPress site pretty shortly, and you would notice these changes too. I will also reduce/delete/hide some of my old posts as I find them very cringy! I would still keep the ones that I find are still nice and interesting to have. For any topic that you would like me to talk about please let me know down in the comments. I may do a Q&A soon too in the future; let’s see. 😀
P.S. The past posts I have on this blog, I have been using “Royalle” – but this was only a screen name. From now on, I will be using my real name.
I find it quite bizarre that there are a lot of mysteries and confusions and “weirdness” in the many wonders of mathematics. One example would be the fact that 0.999… = 1. This means that the number 0.9, followed by an infinite number of 9s, are all equal to 1. But not in the sense that this number is rounded up to 1. It is just equal to 1. But how could that be? We have all learned from middle school that the comparison of decimals involves comparing the integral part first before comparing the decimal part. And in doing so, the greater whole number, the greater its value; and then comparing the decimal part digit after digit after the decimal point. But in this case it seems that 0.999… is of a smaller value since its whole number value is 0 and 1 has an integral part of 1; this meant that 1 would have been greater number. But it seems that there exists a proof that proves that they are indeed both equal:
Let x = 0.999… Therefore, 10x = 9.999… (Multiplying by 10 means that you have to move the decimal point one place to the right). Also if you subtract these two numbers, we have (10x-x) = (9.999…-0.999…). Simplifying it, we have 9x = 9. (The decimal portion of both are both identical; hence they cancel out). Dividing both sides by 9, x = 1. And by transitive property, if x = 0.999… and x = 1, then it must be that 0.999… = 1.
There doesn’t seem to be an error in the proof; all it took was a little Algebraic Magic. However it still seems erroneous at first glance. How come a number with an integral part of 0 be equal to 1? 1.000… = 1 I may say seems more valid, but not 0.999… = 1. And that’s where the problem with infinity arises. Remember that there are an infinite number of 9s after the decimal point. This means that there is no last digit to this number. Think about it; what number would you add to 0.999… so that you can reach the value of 1? Well, that would be 0.000… where the last digit has to be 1; or is it 0.000…1 and that there’s an infinite number of 0s between the decimal point and 1? But how could this be the case since we have already talked about that there is “no last digit”. If your number contains a finite number of 0s instead of an infinite number of 0s, then adding this to 0.999… will result into a number greater than 1. So instead, we expect to add 0.000… instead (infinite number of 0s after the decimal point) to 0.999… to produce 1. But 0.000… is also equal to 0. And adding any number to 0 is always the number itself, which is 0.999… Then again, we are using the transitive property which equates that this number 0.999… is indeed equal to 1.
This is all linked to the peculiar, yet magnificent power of infinity. Here’s another one: how many types of infinity are there? Perhaps I could be more specific by saying that there are a lot of infinities out there that exist, much much greater than other infinities. Here’s an example: how many positive integers are there? The set of all positive integers contains 1, 2, 3, and so forth. And now how many positive real numbers are there? Well, this is a bit much harder since the set of positive integers is just a subset of the set of all positive real numbers. Ok so if we want to list the set of all positive real numbers, we have all these positive integers. What else then? Well, there’s 0.1, 0.2, 0.3,… 0.9. Oh but wait, I think we missed something: 0.01. It, too, is a positive real number. So 0.02, 0.03, …, 0.09 also count. But what if I tell you that you missed another positive real number, which is 0.001? With that said, our listing methods seem to be resulting into a failure. Hence, even if there is an infinite number of elements in this set, it is of a greater cardinality (the number of elements in a given set) than the cardinality of the set of positive integers. Hence, we say that the set of positive real numbers is uncountably infinite and the set of all positive integers is countably infinite. And being uncountably infinite over countably infinite provides proof that there are indeed infinities much greater than others.
There are yet a lot of “weirdness” in maths, and many of them are said to be linked with infinity. But just looking at it, it just seems so beautiful! Ever wonder why the slope of a vertical line on a Cartesian plane is undefined? Ever wonder why the sum of a series tends to converge (meaning to approach a certain definitive number), while others tends to diverge (the opposite of converge)? And have you ever wondered (elementary question) why one is not able to give a definitive number when dividing by 0? All these questions lie to some of the foundations of infinities and I find these very captivating. But yet again, there are still other “mysteries” out there in Mathematics that I also find attractive. All these are to be discussed and explored further in my future blogs.
Date of Post: 12.27.16