Re: The modern mathematical concept of infinity is ...

On 2 Feb, 19:25, Wolfgang Fuckenheim wrote:

There is a simply proof to show that they do: The sequence of all
natural numbers cannot be larger than a natural number

A sequence larger than a number? A category mistake surely.

Theorem: For all n in N: the initial segment {1, 2, 3, ..., n} is
finite and has cardinality n.

So, if there should be an actually infinite set
then it
is forced to contain elements that are not subject of my theorem.

So Fuckenheim regards the observation that {1,...,n}
has n elements "his" theorem. Certainly the ego has landed :-(

So let's analyse this utterance. Now
"elements that are not subject of my theorem" are presumably
natural numbers. So Fuckenheim asserts that any "actually" infinite
sets can't contain natural numbers. Proof by fiat!
.

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