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March 19th, 2018, 04:22 PM   #1
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Cantor's Diagonal Argument and Infinity

If infinity means endless, you can never get to the end of CDA.
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March 19th, 2018, 04:52 PM   #2
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There's no "end" of the integers, either.
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March 19th, 2018, 04:53 PM   #3
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March 19th, 2018, 05:07 PM   #4
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Quote:
Originally Posted by zylo View Post
If infinity means endless
It doesn't though...
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March 19th, 2018, 05:14 PM   #5
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If infinity means endless, you can never get to the end of CDA.
Infinity, infinite, and endless are synonymous. But if it makes you happy:

If infinite means endless, you can never get to the end of CDA.
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March 19th, 2018, 05:20 PM   #6
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Infinity, infinite, and endless are synonymous.
The ordinal $\omega+1$ has an end and is infinite.
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March 19th, 2018, 05:43 PM   #7
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An increasing sequence of Natural numbers either ends (finite), or doesn't (infinite),

1,2,3 is a finite sequence (ends)
1,2,3,4........ is an infinite sequence (endless)
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March 19th, 2018, 05:50 PM   #8
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An increasing sequence of Natural numbers either ends (finite), or doesn't (infinite),

1,2,3 is a finite sequence (ends)
1,2,3,4........ is an infinite sequence (endless)
Sure, and there are also infinite sets which do end.
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March 19th, 2018, 05:58 PM   #9
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Sure, and there are also infinite sets which do end.
Please give an example of an infinite sequence of binary digits which ends.
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March 19th, 2018, 06:32 PM   #10
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Please give an example of an infinite sequence of binary digits which ends.
The ordinal $\omega +1$
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