#Well Ordering Property Doubt

15 messages · Page 1 of 1 (latest)

surreal sage
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Well Ordering Property states -
Every non-empty subset of N has a least element.
But in this proof, (the green underlined part) it is already considered T to have a least element say m as T is a finite (non-empty) subset of N. Isn't that logically poor? The proof is using an argument of considering T (non-empty subset) and it has a least elment. Please, can someone help me out here.
Is there any alternative proof for Well Ordering Property?
OR This proof is actually correct. Am I wrong in understanding this proof?

Screenshot_2025-02-11_065910.png
rain kestrelBOT
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sly shore
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Which you can do by exhaustion.

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Or induction.

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They just didn't expect you to doubt that a finite set has a least element.

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Because... it's finite. You literally can just compare all the elements.

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@surreal sage Following?

surreal sage
sly shore
surreal sage
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Oh sorry, I forgot to close it 😅

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+close

daring shellBOT
# surreal sage +close
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# daring shell

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