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Comments
It is impossible. This can be "proven" with a fallacious "proof". You could also make your own "mathematics" wherein "1=2" holds. However, that "mathematics" would be inconsistent with the conventional mathematics.
An example of a kind of mathematics where 1=2 holds, would be looking at the fractional part of a real number (sometimes also known as working modulo 1).
Recall that ⌊x⌋ is the greatest integer function, which gives you the integer part of a number. The fractional part of a (positive) real number is given by {x}=x−⌊x−⌋. You should be able to verify that the basic arithmetic operations still hold, and is consistent in the equivalence class.
This was popular in the past especially when logarithms were used to multiply large numbers, and looking at the fractional part of the logarithm gives you the initial starting digits. With the invention of calculators, it has fallen out of use and is now mainly used by computers to determine rounding.
It is provable..but the reason why the proof breaks down is very obvious, basic and this proof is foolish :P The proof goes like this. we know that (a2−b2)= (a+b)(a−b) let us consider a=b
we have (a2−a2) = (a+a)(a−a) [This is where everything gets foolish]now, a(a−a) = (a+a)(a−a) [Ridiculous] cancelling (a−a) on both sides, we are left with
a = a+a or a=2a now cancelling a on both sides, 1 = 2 :P
Easy Math Editor
This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.
When posting on Brilliant:
*italics*or_italics_**bold**or__bold__paragraph 1
paragraph 2
[example link](https://brilliant.org)> This is a quote# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"\(...\)or\[...\]to ensure proper formatting.2 \times 32^{34}a_{i-1}\frac{2}{3}\sqrt{2}\sum_{i=1}^3\sin \theta\boxed{123}Comments
It is impossible. This can be "proven" with a fallacious "proof". You could also make your own "mathematics" wherein "1=2" holds. However, that "mathematics" would be inconsistent with the conventional mathematics.
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An example of a kind of mathematics where 1=2 holds, would be looking at the fractional part of a real number (sometimes also known as working modulo 1).
Recall that ⌊x⌋ is the greatest integer function, which gives you the integer part of a number. The fractional part of a (positive) real number is given by {x}=x−⌊x−⌋. You should be able to verify that the basic arithmetic operations still hold, and is consistent in the equivalence class.
This was popular in the past especially when logarithms were used to multiply large numbers, and looking at the fractional part of the logarithm gives you the initial starting digits. With the invention of calculators, it has fallen out of use and is now mainly used by computers to determine rounding.
It is provable..but the reason why the proof breaks down is very obvious, basic and this proof is foolish :P The proof goes like this. we know that (a2−b2)= (a+b)(a−b) let us consider a=b we have (a2−a2) = (a+a)(a−a) [This is where everything gets foolish]now, a(a−a) = (a+a)(a−a) [Ridiculous] cancelling (a−a) on both sides, we are left with a = a+a or a=2a now cancelling a on both sides, 1 = 2 :P
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The reason that this fails is because we can't divide by a−a=0.
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yeah..
We can "Proof that 0 = 1" ( :) ) then add 1 for both sides to obtain 1=2.
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No dude, read that proof properly. it says it is incorrect. you're asked to find out where the mistake is...
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I know.
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then
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It is impossible to prove that 1=2 with a correct proof.
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no, it can be proved correctly, read the first comment. It sums up the situation pretty nicely.
Dude, stop trying to spew fraudulent material. It's not even a proper proof.
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Chill out everybody. I'm pretty sure he was just making a joke. Hence the emoticon in the parentheses.
Zi Song,the method used to obtain that proof wouldn't work for 1 and 2