- published: 13 Jul 2016
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In mathematics, certain kinds of mistaken proof are often exhibited, and sometimes collected, as illustrations of a concept of mathematical fallacy. There is a distinction between a simple mistake and a mathematical fallacy in a proof: a mistake in a proof leads to an invalid proof just in the same way, but in the best-known examples of mathematical fallacies, there is some concealment in the presentation of the proof. For example, the reason validity fails may be a division by zero that is hidden by algebraic notation. There is a striking quality of the mathematical fallacy: as typically presented, it leads not only to an absurd result, but does so in a crafty or clever way. Therefore, these fallacies, for pedagogic reasons, usually take the form of spurious proofs of obvious contradictions. Although the proofs are flawed, the errors, usually by design, are comparatively subtle, or designed to show that certain steps are conditional, and should not be applied in the cases that are the exceptions to the rules.
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First the Earth was flat
But it fattened up when we didn't fall off
Now we spin laps around the Sun
Oh the gods lost 2-1
The host of Heaven pointed out to us from light years away
We're surrounded by a billion galaxies
Things are not always, things are not always how they seem
Will you be ready (will you be ready?)
The interim of life has got you tiptoed and pinning all your hopes on the top dog of dreams
You're not alone in this
The polyfilla way looks strong in the weakness of the gaps
Things are not always, things are not always how they seem
They don't turn out always, don't quite turn out always how we think
Will we be ready (will we be ready?)
I'm dying to know what's in your head
I'm dying to know how it all got in there
I'm dying to know, to help make some sense of it all
I'm dying to know, tell me is it my fault?
And I care about you darling
And I care about you
Course I care about you
More than anyone else
Things are not always, things are not always how they seem
They don't turn out always, don't quite turn out always how we think