Odd or Even?

For the discussion of math. Duh.

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HiThisIsMe
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Odd or Even?

Can anyone prove that 1 is an even number? In any case you can think of.

gmalivuk
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Re: Odd or Even?

Nope, not unless you define "even" to mean something completely different.
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doogly
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Re: Odd or Even?

Somerville is doing even side of the street parking during snow emergencies this year, but not on streets where you can already only park on one side, so for this winter 1 counts an even number.

Chew on that Gmal, I totally nailed this one.
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elasto
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Re: Odd or Even?

gmalivuk wrote:Nope, not unless you define "even" to mean something completely different.

Naw.

You can totally keep the same definition of 'even'.

You merely have to use a new definition of 'prove'.

Spoiler:

Sizik
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Re: Odd or Even?

a = b
a2 = ab
a2 - b2 = ab - b2
(a + b)(a - b) = b(a - b)
a + b = b
2b = b
2 = 1
Since 2 is even, and 2 = 1, then 1 must be even.
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Zohar
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Re: Odd or Even?

Sizik wrote:Since 2 is even, and 2 = 1, then 1 must be even.

You can also use the Banach-Tarski theorem.
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Eebster the Great
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Re: Odd or Even?

You don't have to change the definition of "even," just use a different one. f(x) = 1 is an even function, so it makes sense to say "1 is even" in that respect.

doogly
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Re: Odd or Even?

oooooooooo that is even better than the parking shit
LE4dGOLEM: What's a Doug?
Noc: A larval Doogly. They grow the tail and stinger upon reaching adulthood.

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drachefly
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Re: Odd or Even?

Only if this particular instance of 1 is also deep and crisp.

Mike Rosoft
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Re: Odd or Even?

You can prove that 1 is even, if you work in an inconsistent system. (By definition, an inconsistent system is a system where every statement can be proven; equivalently, it is a system in which there exists statement A such that both "A" and "not A" can be proven; any statement can be proven from "A & not A".)

[edit:]
This is a deeper statement than it seems, because it is very difficult to prove that a particular system is consistent. In particular, a system which includes integers with the usual (Peano) axioms is strong enough to "describe itself" (i.e. you can use integers to represent mathematical formulae and relations between them, such as "formula X can be proven from such-and-such axioms"); such a system cannot prove its own consistency, unless it is itself inconsistent.

Flintstone
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Re: Odd or Even?

1 Pair. Now it's even .