If my students were paying attention to my discussions about methods of proof, my favorite topic in discrete math, I think they'll find this interesting, too.
All numbers are equal
Theorem: All numbers are equal.
Proof: Choose arbitrary a and b, and let t = a + b.
Proof: Choose arbitrary a and b, and let t = a + b.
Then
a + b = t
(a + b)(a - b) = t(a - b)
a^2 - b^2 = ta - tb
a^2 - ta = b^2 - tb
a^2 - ta + (t^2)/4 = b^2 - tb + (t^2)/4
(a - t/2)^2 = (b - t/2)^2
a - t/2 = b - t/2
a = b
So all numbers are the same, and math is pointless.
Woah! What just happened here?
Woah! What just happened here?
I hope some of my students will find this and tell me what exactly happened there. Haha. Cute, isn't it?
2 comments:
hmm... something's fishy fishy... the conclusion was a = b, therefore, by reverse engineering (ngek!), you can't multiply both sides of the equation by (a-b) kasi...
a = b
a - b = 0
so any number multiplied by 0, zero jud... rights? sorry nag-comment ko without permission... heheheh... ciao!
hi frix,
ok ra kaayo magcomment oi...
it is not assumed that a = b. a and b are any real number.
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