## Forum Posts

Reacher Miao

Jun 10, 2018

In MCV4U1 Forum

I like how Unit 8 on Mr.G's Calculus website says "Coming soon" for the last three videos. Everything is coming soon, everything you wanted. But then there is always something leaving earlier, which we should cherish but we don't really care until we care. Like... I am pretty sure everyone can find his/her own examples and no sooner will they realize that than the things come soon become real and solid, you might be disappointed, or you might be more surprised. We can't absolutely be perfect at everything, in fact, no one can be perfect at anything, and it doesn't really matter too much to which level you are at. It does not matter ultimately, because we are literally like stardust, nothing behind us, everything ahead of us, none makes us more important and we will eventually be forgot by everyone and everything, so I guess the thing I am trying to say is, no one has to be too concerned about the things coming soon, or too excited, because it's probably not worth that much. And it's been a great half of a year to spend time here and there with everyone here and there and who knows whats gonna happen in the future and ultimately they dont matter. So yeah, everyone can try to make a difference on a small scale, and live like bliss-fast before they know they get old, and it's probably what will happen. Don't get sad about that, because it's not even worth it to be sad about the fact that a lot of things will not matter anymore and a lot of things that dont matter now will matter in the future. Yeah by the way this is my bandcamp website feel free to check out my music or purchase them it doesnt matter much to me but hey why not share it while I can so here it is: https://reachermiao.bandcamp.com (trying to copy and paste? sorry, life is not that easy) (and I guess this is the point, ultimately?) I generally try to be a nice person, so forgive me if I was not, and I wish everything good luck, not just everyone but like even mathematics and metaphysics. Then feel free to comment anything you like because it's probably worth it. And by the way if you are determined to do something, please keep it going and don't give up until you have last cent in your pocket spent for it. By then I might support you if it's worth it, as long as I make some money, email me if that happens: nymiaoshuhan@gmail.com Reacher Miao Ends this with a little poem Coming soon, my life, everything I have lived so far, and everything ahead of me will be lived by me. Coming soon, my death, everything that is worth living for, and the end just a happy smile because that's all that is needed

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Reacher Miao

Mar 14, 2018

In MCV4U1 Forum

Since it's March 14th today, I am going to celebrate it somehow. So I will do a proof on why the heck √2 is irrational( like literally a serious proof). (As if it's related...) Proof: Assume that √2 is rational, which would imply that it could be expressed as a/b(you have to believe me that this holds true for all rational numbers), where a and b are relatively coprime integers( that means they are pretty close, like a = 1.4 something b). Okay, now we have an equation: √2 = a / b It would be more interesting if we square both side. So we get: 2 = a**2 / b**2 (excuse me for my manner using ** for the square operation. It doesn't mean bad words, just a standard way of expressing in a high level machine programming language like Python, which you guys will probably see in Uni). Great! What does this mean? It means that the square of a is like twice the square of b. Before we say anything, remind me that a and b are relative prime numbers, which means they are coprime, which means that they can not be all even numbers(Hint: coprime numbers can not have common factors besides 1, two even numbers mean that they all have a common factor of 2). Alright, what the heck does it mean that the square of a is twice the square of b? WELL, a**2 = 2(b**2) - The term 2(b**2) is even. - The square of a is gotta be even. Only even number's square is even. Therefore a is gotta be an even number. Let a = 2c. We get 4(c**2) = 2(b**2). Therefore, b**2 = 2(c**2). - Same logic we used previously, since 2(c**2) is even, b**2 is even, therefore b is an even number. Heck, did we not just mention that "a and b can not be two even numbers" before we say anything? So here we go, since there is no rational number a and b that would make √2 = a/b, √2 is irrational. Quod erat demonstrandum What we proved could be expressed in the following first-order-logic expression: ¬ (∃ a ∈ N) (∃ b ∈ N) [ 2 = p**2 / q**2 ] What's cool about it is that it allows us to see what given conditions, properties, and target equation very clearly. Which is very helpful to see how logical mathematics can be. Which is why pi is not a rational number. Could someone prove it in a similar way? Some reference + follow-up reading: https://en.wikipedia.org/wiki/List_of_logic_symbols https://artofproblemsolving.com/wiki/index.php?title=Proof_by_contradiction

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Reacher Miao

Feb 24, 2018

In MCV4U1 Forum

We live with continuity, but we do discontinue sometimes. When our daily life function gets irrupted, we tend to stop. It's the decision we make that decides either we go up from this point on or we go down. Derivatives, the short cut we know doesn't work. Not even limits. It can't deal with this seemingly impossible one-sided-limit-doesn't-equal-the-other situation. Now we are back to the most basic thing, that one glitch in life that we have to discover which is completely different from everything else. Are we going to cry a little? Maybe. Are we going to ask for help? Possibly. In the end, we would somewhat come up with a possible solution, and let it go. In the end, nothing matters. When you look back at the ripples in your life, it's so small that we forget sometimes, how much we have tried and tried. The less failures you remember, the more genuine those ripples are. Happiness is sometimes gained through breaking the limits, and continuity. It is not just being comfortable. If mankind were comfortable all the time, Canada wouldn't be discovered. It is one little glitch, that mankind evolution started. We develop, and we jump over those discontinuities and go upwards, against the wind. I can't possibly address the issue with becoming an adult with all kinds of problems we have to deal with, the fact that we are going to stop and do those discontinuities. It's not that we are all what we've got. It is what You Don't Know makes you move forward, not just in math problems, but in life, with a cautious and courageous mind, with a little hope for the sparks of new ideas generate within our limited mind, with nothing comparable to what mankind knows. Back to the problem, we would move on from the discontinuity, and go back to our life. It might suck for a bit, but we will be functioning normally again, and again, and again.

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# Reacher Miao

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