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From: Richard Heathfield <rjh@cpax.org.uk>
Newsgroups: comp.theory
Subject: Re: Cantor Diagonal Proof
Date: Sun, 6 Apr 2025 09:33:24 +0100
Organization: Fix this later
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On 06/04/2025 09:23, wij wrote:
> On Sun, 2025-04-06 at 09:11 +0100, Richard Heathfield wrote:
>> On 06/04/2025 08:49, wij wrote:
>>> On Sun, 2025-04-06 at 08:36 +0100, Richard Heathfield wrote:
>>>> On 06/04/2025 08:15, wij wrote:
>>>>
>>>> <snip>
>>>>
>>>>> Simply put, repeating decimals are irrational.
>>>>
>>>> Simply put, an irrational number is one that can't be expressed
>>>> as the ratio of two integers.
>>>
>>> Prove it.
>>
>> The clue is in the name.
>>
>> Thus quoth Wolfram: "An irrational number is a number that cannot
>> be expressed as a fraction p/q for any integers p and q."
>> <https://mathworld.wolfram.com/search/?query=irrational+number>
>>
>> When you've persuaded Wolfram that they're wrong, call.
>>
>> What is this, Give A Crank A Home Week?
>>
> 
> Obviously, you don't even understand what 'definition' is, neither.

Obviously. And equally obviously, I don't understand that 1 and 3 
are infinite (non-natural).

But /you/ do. "From Theorem 2 and Axiom 2, if x can be expressed 
in the form of p/q, then p and q will be infinite numbers 
(non-natural numbers ). Therefore, x is not a rational number. 
And since a non-rational number is an irrational number, the 
proposition is proved."

Presumably you believe the above, which proves that you can't 
count up to 1, not even if you take your socks off. Well done, you.

-- 
Richard Heathfield
Email: rjh at cpax dot org dot uk
"Usenet is a strange place" - dmr 29 July 1999
Sig line 4 vacant - apply within