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Wednesday 23 February 2011
Everything you learned in Math class is wrong
Here's proof that 2=1
a = b
So...
a^2 = b^2
and
a^2 - b^2 = ab - b^2
and if we unpack that....
(a-b)(a+b) = b(a-b)
a + b = b
Which means that
b + b = b
2b = b
2 = 1
5 comments:
Anonymous
said...
No.... everything _you_ thought you learned in math class is wrong, if that is what you learned.
5 comments:
No.... everything _you_ thought you learned in math class is wrong, if that is what you learned.
In order to get from
(a-b)(a+b) = (a-b)b
...with a=b,
(0)(a+b) = (0)b
... you can't divide by 0 to get
a+b = b.
So the rest is gibberish.
Oh, of course...I didn't see that.
Not just the workings are wrong, the start is wrong.
The equation 2=1 commits the error of the truth of premises in logic.
While the premise is structurally sound i.e., 2=1 it is a false premise. A structurally sound but false premise will only lead to a false conclusion.
For example:
All cattle have five legs.
Friesians are cattle.
Therefore, Friesians have five legs.
Garbage in, garbage out. QED.
Like the following false premise:
England > Australia
Ireland > England
Therefore:
Ireland > Australia
Wait a minute... everything you learned in Test Match Special is wrong
Well, the first Anonymous disagrees with the second Anonymous. It happens. We all survive somehow.
Everything in
a = b
So...
a^2 = b^2
and
a^2 - b^2 = ab - b^2
and if we unpack that....
(a-b)(a+b) = b(a-b)
is 'structurally' fine, starting with the assertion that a=b.
It was only the step beyond that, that went astray and led to garbage.
Wasn't garbage in. It became garbage along the way. That is why issues like that are potentially misleading.
Happens all the time in modeling.
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