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**Tryphadz** · 03-14-2009, 07:17 PM

a cannot equal b because algebra states that a must only equal a and b must only equal b.

Not quite - the start of the 'puzzle' is perfectly valid, as it's essentially saying "one has two variables, a and b, and they are equal to each other". To argue otherwise, would be saying that the function y = x cannot be plotted - and it quite obviously can!

this suggests that (a+b) is equal to b which again at the top of the equation is stated that a=b so how can a+b = b

Well that was the point of the 'puzzle' - i.e. you end up 'proving' that 2 =1

Division by zero is not allowed, so all calcuations after that are irrelevant.

*Ding* And we have our winner!

Edit:

Yeah that's it, in "classic" algebra math rules the following mistake is made:

When dividing by (a-b) you're stating:

A+b = b OR a-b = 0

The last one is often forgotten, but is true in this case, since a = b

The first one (a + b = b) is also true, as there is a number out of the set of real numbers for which there is defined answer: a = b = 0. It's the part where both sides need to be divided by (a - b) that isn't permitted, as division by zero doesn't have a defined solution in real number algebra.

03-14-2009, 07:17 PM	#15
Tryphadz Join Date Oct 2005 Posts 475 Senior Member	a cannot equal b because algebra states that a must only equal a and b must only equal b. Not quite - the start of the 'puzzle' is perfectly valid, as it's essentially saying "one has two variables, a and b, and they are equal to each other". To argue otherwise, would be saying that the function y = x cannot be plotted - and it quite obviously can! this suggests that (a+b) is equal to b which again at the top of the equation is stated that a=b so how can a+b = b Well that was the point of the 'puzzle' - i.e. you end up 'proving' that 2 =1 Division by zero is not allowed, so all calcuations after that are irrelevant. Ding And we have our winner! Edit: Yeah that's it, in "classic" algebra math rules the following mistake is made: When dividing by (a-b) you're stating: A+b = b OR a-b = 0 The last one is often forgotten, but is true in this case, since a = b The first one (a + b = b) is also true, as there is a number out of the set of real numbers for which there is defined answer: a = b = 0. It's the part where both sides need to be divided by (a - b) that isn't permitted, as division by zero doesn't have a defined solution in real number algebra.
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