Prove All Numbers Equal: No 0 Needed!

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Discussion Overview

The discussion revolves around a claim that all numbers are equal, supported by a proof that purportedly does not involve the number zero. Participants analyze the steps of the proof, focusing on the mathematical validity of the operations performed and the implications of taking square roots.

Discussion Character

  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant claims to have proven that all numbers are equal without using zero, presenting a series of algebraic manipulations.
  • Another participant points out an error in the proof, specifically regarding the addition of terms that leads to the conclusion that a equals b.
  • A different participant argues that the manipulation of terms does not create problems, suggesting that the equality remains valid.
  • Concerns are raised about the implications of taking square roots, with one participant asserting that the square root operation introduces an additional solution that must be considered.
  • There is a discussion about the nature of square roots, with one participant emphasizing that both positive and negative roots should be accounted for in the proof.

Areas of Agreement / Disagreement

Participants express disagreement regarding the validity of the proof and the mathematical steps involved. Multiple competing views remain about the correctness of the operations and conclusions drawn from them.

Contextual Notes

Participants highlight potential issues with the proof, including the treatment of zero and the implications of taking square roots, but do not resolve these concerns.

amits
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All numbers are equal :D

heres the latest proof and it doesn't involve 0 anywhere. no term like (a-b) is involved unlike other similar proofs

-ab = -ab
=> a^2 - a^2 - ab = b^2 - b^2 - ab
=> a^2 - a(a+b) = b^2 - b(a+b)
=> a^2 - a(a+b) + (a+b)^2/4 = b^2 - b(a+b) + (a+b)^2/4

as (x-y)^2 = x^2 - 2xy + y^2,

[a - (a+b)/2]^2 = [b - (a+b)/2]^2

taking square roots,

a - (a+b)/2 = b - (a+b)/2
a = b

hence proved :D

now with all numbers having been proved equal without involving "0" anywhere, what's the need to study anything :D

just noticed, this is my 1st post here after 7 years :o
 
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You can't take square roots. x^2 = y^2 does not imply x = y
If it did, this would have been your 7th post after 1 year.
 


Your second line contains an error. You added a^2 - a^2 to one side of the equation, but b^2 - b^2 to the other side. The only way for this to leave the equality unchanged is for a to equal b... so it's no surprise that you find out later that a = b.

- Warren
 


amits said:
=> a^2 - a^2 - ab = b^2 - b^2 - ab

This is the same as
a^2 + b^2 - ab = b^2 + a^2 - ab , which don't think should create any problems.
 


amits said:
[a - (a+b)/2]^2 = [b - (a+b)/2]^2

taking square roots,

a - (a+b)/2 = b - (a+b)/2
This is your error. Taking square roots leads to

a-(a+b)/2=b-(a+b)/2
or
a-(a+b)/2=-(b-(a+b)/2)

The former yields a=b. The latter yields a+b=a+b.
 


chroot said:
Your second line contains an error. You added a^2 - a^2 to one side of the equation, but b^2 - b^2 to the other side. The only way for this to leave the equality unchanged is for a to equal b... so it's no surprise that you find out later that a = b.

- Warren
That step is correct. It's just adding zero to each side.
 


chroot said:
Your second line contains an error. You added a^2 - a^2 to one side of the equation, but b^2 - b^2 to the other side. The only way for this to leave the equality unchanged is for a to equal b... so it's no surprise that you find out later that a = b.

- Warren

it isn't an error. i added a^2 + b^2 to both sides

-ab = -ab
a^2 + b^2 - ab = a^2 + b^2 - ab

a^2 - a^2 - ab = b^2 - b^2 - ab

also a^2 - a^2 = 0 & b^2 - b^2 = 0, so adding that doesn't make a difference
 


Jimmy Snyder said:
You can't take square roots. x^2 = y^2 does not imply x = y
If it did, this would have been your 7th post after 1 year.

yes, you are right. a number always has 2 square roots, 1 positive & 1 negative
 
Last edited by a moderator:


You got it wrong.
2^2 = (-2)^2
when you have sqr root you have to have either + or - sign. you only considered + sign. Consider - sign and you will get a+b = a+b
 

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