Odd or Even?

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HiThisIsMe
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Odd or Even?

Postby HiThisIsMe » Fri Nov 18, 2016 10:20 am UTC

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

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gmalivuk
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Re: Odd or Even?

Postby gmalivuk » Fri Nov 18, 2016 1:34 pm UTC

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

Postby doogly » Fri Nov 18, 2016 1:49 pm UTC

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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Re: Odd or Even?

Postby elasto » Fri Nov 18, 2016 2:41 pm UTC

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'.

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Sizik
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Re: Odd or Even?

Postby Sizik » Fri Nov 18, 2016 3:18 pm UTC

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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Re: Odd or Even?

Postby Zohar » Fri Nov 18, 2016 3:25 pm UTC

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?

Postby Eebster the Great » Fri Nov 18, 2016 7:11 pm UTC

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.

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doogly
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Re: Odd or Even?

Postby doogly » Fri Nov 18, 2016 7:44 pm UTC

oooooooooo that is even better than the parking shit
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drachefly
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Re: Odd or Even?

Postby drachefly » Fri Nov 18, 2016 9:03 pm UTC

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

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Re: Odd or Even?

Postby Mike Rosoft » Thu Dec 29, 2016 3:12 pm UTC

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.

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Re: Odd or Even?

Postby Flintstone » Wed Apr 19, 2017 8:02 am UTC

1 Pair. Now it's even :D .


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