Re: Set Theory: Should You Believe



John Jones wrote:

herbzet@xxxxxxx wrote:
John Jones wrote:
herbzet@xxxxxxx wrote:
[...]
Infinity is a tough nut to crack.

Number is defined by a limit, infinity has no limit and cannot be a
number.

Please go on.

Loosen your belt. Expand!


This 'logic' site generally is like an empty shopping mall on a windy,
rainy sunday afternoon. My posts are studiously ignored, even in a post
challenging mathematics and logics foundations. So I assume you are not
a logician. Which is not as good as being a philosopher anyway.


I think of logic as a branch of philosophy, no?


Infinity in mathematics is challenged by 'finitism' and
constructivism'.
Numbers are constructed, not found. So there is no 'infinite number'.
Infinity, like zero, has no limit. So as a number is defined and
identified by a limit, or by some act (otherwise we could not
distinguish one number from another), then as infinity and xero have no
limit, they are not identifiable as numbers. It is the act of making a
number that identifies a number, and not merely the appearance. The
appearance is called a numeral.


1) It is unclear whether you are speaking for yourself, or
if you are assuming the voice of those whose opinions
you disagree with, or both. Perhaps you wrote in some haste.

2) You are aware, perhaps, that the term "limit" has a precise,
technical meaning in mathematics. It is widely used in
this technical sense, and in particular it has been used
extensively in the construction of some classes of numbers.

In discussion _of_ mathematics, it might be well to find
a synonym to use in its place, if you are not using the
term in this technical sense, in order to keep confusion to
a minimum. Or, alternatively, to make clear in what sense,
exactly, you are using the term.

It is difficult to comment on the substance of your post, since
I am unclear on what it is that you are asserting. Perhaps you
could further explicate? I enjoy reading your writing.

--
hz
.

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