Re: Replacement of Cardinality

Am 07.08.2024 um 01:46 schrieb Chris M. Thomasson:

On 8/6/2024 2:02 PM, Moebius wrote:

Am 06.08.2024 um 22:21 schrieb Chris M. Thomasson:

On 8/6/2024 6:33 AM, Moebius wrote:

Am 06.08.2024 um 04:24 schrieb Chris M. Thomasson:
>

There are infinite[ly many] even[ numbers] and
there are infinite[ly many] odd[ numbers].

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On the other hand, some even numbers are odd. :-)

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;^D 666?
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Ahh zero. I think its even... ;^)
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1, 2, 3, 4, ...
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odd, even, odd, even, ...
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So, the pattern:
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-2, -1, 0, 1, 2
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even, odd, (even), odd, even

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Yes. An integer z is even, iff there is am integer k such that z = 2k.
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Clearly for z = 0 there is an integer k (namely 0) such that z = 2k.
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In other words, an integer z is even if it can be deviede by 2 "without a remainder =/= 0".
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Clearly 0 can be devided by 2 "without a remainder =/= 0": 0 / 2 = 0.
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So 0 is an odd even number? :-)

Hint: This was a joke. :-)
"odd" here is meant in a colloquial sense, while "even" is meant in a technical (math.) sense. :-)

I say even?

Right.  :-)
Though still odd. lol.
Hint: "0 is the oddest even number." (Jim Burns)

Well, both (odd and even) at the same time?

Nope. Just even (math).

This makes me think of signed zero...
 +0
-0
 and just, 0?

Right. (Try it in some computer language of your coice: If 0 == +0 ... amnd If 0 == -0 ...)
But when used in the context of "lim" there is a certain difference. (Still "in a pure technical sense" +0 = -0 = 0."

0 is just zero?

Right: 0 = +0 = -0.
But the NOTATIONS "+0" and "-0" are used in the context of the "lim" notation, to signify if 0 is "approached" vom "right", or from "left".