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Math is not all Powerful

Math lets you do a lot of things. But here are 5 things that Math does not allow you to do:

1) Math does not allow you to divide by zero.

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Because the universe will implode.

Image credit: ESO/M. Kornmesser

2) Math does not allow you to prove every statement.

English: This statement cannot be proved.

Math-speak:

\[ \sim ( 3r:3s: \, (P (r,s) V ( s = g (\text{sub} ( f_2(y))))) \]


3) Math does not allow you to create infinite chocolate

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Because only oranges can be Banach-Tarski duplicated.


4) Math does not allow you to comb a hairy ball.

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This rabbit is doomed to looking unkempt forever. It cannot be combed.

Image credit: Wikipedia Betty Chu

5) Math does not allow you to define a dull number.

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Suppose not. Find the smallest. Then that number is interesting ...


Know of any good paradoxes? Add them to the Paradox page!

Note by Calvin Lin
2 years, 2 months ago

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Math does not allow you to get a girlfriend :P Trevor Arashiro · 2 years, 2 months ago

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@Trevor Arashiro That is so 2013. It only takes 88 dates Calvin Lin Staff · 2 years, 2 months ago

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@Calvin Lin I stand corrected...up to a certain extent.

AND CAN YOU PLEASE EXPLAIN THAT CHOCOLATE GIF TO ME

I watched it for like 4 minutes... But I still don't get if Trevor Arashiro · 2 years, 2 months ago

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@Trevor Arashiro A 5x5 block of chocolate is shown being divided up, re-arranged, and re-assembled back to a 5x5 block of chocolate and one extra piece, which is eaten. This process is continued indefinitely, seemingly generating an infinite number of extra pieces of chocolate. Calvin Lin the comedian intones "Math does not allow you create infinite chocolate" followed by, "Because only oranges can be Banach-Tarski duplicated", the logic being that because an orange is a solid sphere, a duplicate can be created from it by being first divided up into a finite number of (very weird) pieces, which are re-arranged to create two solid spheres (oranges) exactly the same as the original, via the Banach-Tarski theorem. Get it now?

Banach-Tarski Paradox Michael Mendrin · 2 years, 2 months ago

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@Michael Mendrin Oh that explanation looks mad complicated - how much math do I need to know, exactly, to get it?

So wait this implies if you have a solid sphere you can make infinitely more out of it? I've heard of that before but eh don't really get it. I get teh chocolates - took liek a month to figure out off of an analogous triangle problem. But not this Banach-Tarski slice n' dice.

Oh, and I dunno as far as dividing by zero goes; what about complex infinity?

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John Muradeli · 2 years, 2 months ago

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@John Muradeli Banach Tarski is not that bad. There are "simple" constructions which show how to create 2 spheres from 1. I am considering doing a writeup in the near future, and adding it to the Wiki.

The main "paradox" is that volume is not preserved under rotation, unless the set is "measurable". As such, the idea is to cut the ball up into non-measurable parts, and then move them around to change the volume, and then piece them back together again. Calvin Lin Staff · 2 years, 2 months ago

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@Calvin Lin An even simpler example would be having an infinity of mathematicians sitting around in a round table at a restaurant bar. One of the mathematicians is missing his drink, all the others have a drink. So, it's proposed that every mathematician that is \(n\) radians from the luckless mathematician, \(n\) being every positive integer, simply hand his drink to the mathematician one radian next to him. Then all mathematicians have got a drink, and everybody's happy. Michael Mendrin · 2 years, 2 months ago

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@Trevor Arashiro That short peice on most right just look at its bottom left(it contains very small part of 1x1 peices) but see where it joins (it need more chocolate to be perfect 1x1 peice). Its just a trick that at re-assembling the chocolate joins with much greater speed that one cant find the difference Krishna Sharma · 2 years, 2 months ago

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Can you please explain that logic notation? Agnishom Chattopadhyay · 2 years, 2 months ago

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Math do not allow you to find the actual value of pi (not22/7 but 1-1/3+1/5-......) Samruddh Kamath · 1 year, 8 months ago

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@Samruddh Kamath The exact value of \( \pi \) is \( \pi \) itself :) Calvin Lin Staff · 1 year, 8 months ago

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Math does not help you decide when you are going to have an exam:

The last Friday my teacher announced that he will give us an exam on the following Monday, Tuesday or Wednesday and that the exam will be a suprise. I argued that the exam cannot be held on Wednesday because at the end of Tuesday I will know that the exam will be held on Wednesday and therefore it will not be a surprise. By the same arguing the exam cannot be held on Tuesday because at the end of Monday I will know that the exam will be held on Tuesday and therefore it will not be a surprise. So the exam must be held on Monday. I argued that it cannot be on Monday because it will not be a surprise. The exam was on Tuesday and it was a surprise!

See https://en.wikipedia.org/wiki/Unexpectedhangingparadox Pambos Evripidou · 1 year, 1 month ago

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Math's does not allow us to understand universe Aman Baser · 2 years, 2 months ago

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@Aman Baser It's doing a really good job of it so far. What else explains it better? Michael Mendrin · 2 years, 2 months ago

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@Michael Mendrin The problem is that the more we understand about the universe, the more we know how little we understand. Trevor Arashiro · 2 years, 2 months ago

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Maths does not reach the infinite or uncountable. Aarti Doshi · 1 year, 10 months ago

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