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Topic: ? 417 An implication of actual infinity
Replies: 5   Last Post: Jan 12, 2014 4:29 PM

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Ben Bacarisse

Posts: 751
Registered: 7/4/07
Re: ? 417 An implication of actual infinity
Posted: Jan 11, 2014 6:54 PM
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WM <wolfgang.mueckenheim@hs-augsburg.de> writes:

> Am Samstag, 11. Januar 2014 19:49:10 UTC+1 schrieb Ben Bacarisse:

>> > I said quite clearly that I consider only the terms of the sequence of
>> > FISONs, not its limit.

>> You also said of lim(n=1..)[ S_n ] "[i]n the infinite there is no limit
>> set" (mesage ID: <8c904bde-0087-430d-bf5b-261c83ed0bd7@googlegroups.com>)

> Correct.

>> Are you changing your mind? Does the limit set lim(n=1..)[ S_n ] exist?

> No. (But if set theory is the base of arguing, then all S_n must
> exist.)

So, have we found the first thing where you'd tell the students a lie?
In mathematics lim(n=1..)[ S_n ] = N but a student claiming that would
be told it's not true?

(Oddly, lim(n=1..)[ S_n ] is the same as Union(n=1...)[ S_n ] which is equal
N even in WMaths. In some definitions the limit is even defined in
terms of unbounded unions and intersections.)


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