Half the posts over here are trying 2 prove that 1=2 or 0=-1 or

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Discussion Overview

The discussion revolves around attempts to demonstrate paradoxical mathematical statements, specifically the erroneous proofs that suggest 1=2 or 0=-1. Participants explore the implications of assuming two real numbers are equal and the resulting algebraic manipulations.

Discussion Character

  • Exploratory
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant proposes a proof starting with the assumption that a = b, leading to the conclusion that b = 2b, which is presented humorously.
  • Another participant suggests that if a = 0, then the earlier manipulations could imply b = 0.
  • A third participant points out that the step (a-b)(a+b) = b(a-b) is problematic because it involves dividing by (a-b), which equals zero when a = b, rendering the operation meaningless.
  • Further clarification is provided that dividing by zero is undefined in mathematics, reinforcing the error in the initial argument.

Areas of Agreement / Disagreement

Participants generally agree on the error in the manipulations involving division by zero, but there is no consensus on the broader implications or the nature of the initial claims being discussed.

Contextual Notes

The discussion highlights limitations in the algebraic steps taken, particularly the assumption that division by zero can be performed, which is a fundamental issue in the reasoning presented.

toocool_sashi
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half the posts over here are trying 2 prove that 1=2 or 0=-1 or sumthing like that lol so i thought ill try sumthing of that sort too...its silly...but it fascinated me when i was in class 8.

Let a = b where a, b are any 2 real numbers
a^2 = ab
a^2-b^2=ab-b^2
(a-b)(a+b)=b(a-b)
a+b=b
But a = b therefore b = 2b for any real number b

enjoy! don't curse me for wasting ur time when u find the mistae!
 
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...or a=0...
 
a+b=b;
a=b;
so b+b=b
so b=a=0?
 
Answer in white:

"(a-b)(a+b)=b(a-b)"
a-b=0, so it is meaningless to divide both sides by (a-b)
 
Let a = b where a, b are any 2 real numbers

a2 = ab
Subtract both sides with b2 ==> a2-b2 = ab-b2
Simplify ==> (a-b)(a+b)=b(a-b)
divide with (a-b) ==> a+b = b
a=b gives ==> 2b = b

And the error is as said very simple.
 
toocool_sashi said:
(1) (a-b)(a+b)=b(a-b)
(2) a+b=b

to get eq. (2) from eq. (1)

you have to divide both sides by (a-b)
since a=b
therefore, (a-b)=0...

in addition, you have divided two sides by zero...

a number divided by zero is undefined in math...

got ya!
 

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