Proof

[shanmonster]

9 - 24 = 25 - 40
9 - 24 + 16 = 25 - 40 + 16
(3 - 4)² = (5 - 4)²
3 - 4 = 5 - 4
3 = 5

Right?

Comments

[sidruid.livejournal.com]

there are just so many bad mathematical inferences between those lines...
(-1)^2 = (1)^2
but
(3-4 = -1) != (5-4 = 1)

[shanmonster.livejournal.com]

Oh noes!

Next up, 1 + 1 = 3.

[sorceror.livejournal.com]

This is the same proof used to demonstrate that 1=2.

And with that, the entire universe collapses in a puff of false logic.

[twopiearr.livejournal.com]

see, the easy way to avoid all this angst is just to remember that there is no way to prove that 1=1 without using the very rules founded on the assumption that 1=1. Ergo, all of mathematics is little more than a complex system of faith.

[the-s-guy.livejournal.com]

Start by defining "1"...

[sageincave.livejournal.com]

There seems to be a bit of a leap between the 2nd and 3rd lines....

[the-s-guy.livejournal.com]

Actually, they do match, both numerically and using the (x-y)^2 = x^2-2xy-y^2 algebraic equivalence.

The problem lies in the change between the third and fourth lines. Just because x^2 = y^2 does not necessarily mean that x=y, although in an integer or real numberspace it will mean that x=±y. In this case x=-y, but the fourth line takes it as x=y instead. Once you have that divergence, you can prove that anything equals anything else.

[(Anonymous)]

Here is one that works


x = .9999999999 (repeating -close to but never reaching one)
10x = 9.9999999999
10x - x = 9.9999999999 - .999999999999
9x = 9
x = 1 (wait a moment - read first line)