Sujet : Re: Contradiction of bijections as a measure for infinite sets
De : james.g.burns (at) *nospam* att.net (Jim Burns)
Groupes : sci.mathDate : 26. Mar 2024, 01:04:30
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <f8c34b23-20d7-4bd4-b40f-4b990f71dbde@att.net>
References : 1 2 3 4 5 6
User-Agent : Mozilla Thunderbird
On 3/25/2024 6:11 PM, WM wrote:
Le 25/03/2024 à 20:38, Jim Burns a écrit :
[...]
>
You cannot add a natural number to ℕ.
You cannot add a natural number to ℕ ==
ℕ holds all sizes of sets for which
changing by one element changes the set's size.
ℕ doesn't have any of those sizes.
ℕ isn't a set for which
changing by one element changes the set's size.
But a bijection of ℕ with |E = {2, 4, 6, ...}
would prove that both sets have
the same number of elements.
ℕ and 𝔼 aren't sets for which
changing by one element changes the set's size.
Adding an element to |E destroys this state
1 ⟼ 2
n ⟼ n+2
𝔼∪{1} ⇉ 𝔼
and shows ℕ is larger than ℕ.
Contradiction!
| CAESAR (recovering his self-possession):
| Pardon him, Theodotus:
| he is a barbarian, and thinks that
| the customs of his tribe and island are
| the laws of nature.
|
George Bernard Shaw, "Caesar and Cleopatra" (1898)
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