Re: Replacement of Cardinality

On 8/15/2024 10:57 PM, Moebius wrote:

Am 16.08.2024 um 07:50 schrieb Moebius:
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Of course, _if_ we already have introduced the real numbers (i.e. IR) we may define
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       √2 = the real number x such that x^2 = 2 ,    (*)
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_after_ we have shown that there is exactly one x e IR such that x^2 = 2.
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From (*) we get immediately: (√2)^2 = 2

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Now we may assume that there are natural numbers n,m such that √2 = n/m.
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(...)

 The infinite convergents of continuous fractions can describe sqrt(2) up to any desired precision?