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Anonymous Tue 08 Feb 23:19:56 2022 No.14203402 View Reply Original Report

Quoted By: >>14203465 >>14203494 >>14203516 >>14203660 >>14203689

Is the set of negative integers well ordered??? But it doesn't have a least element... yet it has the greatest element...

?????? -_(*_*)_-

Anonymous

Anonymous Tue 08 Feb 2022 23:36:19 No.14203465 Report

Quoted By: >>14203483

>>14203402
You could argue the same for whatever the positive integers are.

Anonymous

Anonymous Tue 08 Feb 2022 23:38:56 No.14203483 Report

Quoted By:

>>14203465
I'm talking in terms of infinite sets

Anonymous

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Anonymous Tue 08 Feb 2022 23:39:33 No.14203484 Report

Quoted By:

We put zero in the wrong place on the number line.

Anonymous

Anonymous Tue 08 Feb 2022 23:41:20 No.14203494 Report

Quoted By: >>14203827

>>14203402
it's not well ordered, but you can well order it by defining <= the other way around

Anonymous

Anonymous Tue 08 Feb 2022 23:45:42 No.14203516 Report

Quoted By: >>14203529

>>14203402
Yes, a well ordered set doesn't need to have a least element

Anonymous

Anonymous Tue 08 Feb 2022 23:49:14 No.14203529 Report

Quoted By: >>14203618

>>14203516
The definition of a well ordered set is a non-empty one that has a least element, and clearly the negative numbers are not empty, so it cannot be well ordered since there is no least element.

Anonymous

Anonymous Wed 09 Feb 2022 00:10:20 No.14203609 Report

Quoted By:

Do we assume he had $60 or $0 in the first place? Because that makes all the difference in what the answer will be.

Anonymous

Anonymous Wed 09 Feb 2022 00:12:18 No.14203618 Report

Quoted By: >>14203658

>>14203529
What about negatives with negative infinity

Anonymous

Anonymous Wed 09 Feb 2022 00:23:43 No.14203658 Report

Quoted By: >>14203687

>>14203618
-Infinity isn't an element of the set.

Anonymous

Anonymous Wed 09 Feb 2022 00:23:48 No.14203660 Report

Quoted By: >>14203827

>>14203402
Depends on the order you chose. Using the standard order, no. With some other order, sure.

Anonymous

Anonymous Wed 09 Feb 2022 00:35:20 No.14203687 Report

Quoted By:

>>14203658
I know that's why I'm talking about it like it's a different thing from just the negatives

Anonymous

Anonymous Wed 09 Feb 2022 00:36:02 No.14203689 Report

Quoted By: >>14203693

>>14203402
The standard ordering on the integers is not well ordered.
However, the following ordering <_R is well ordered:
For positive x, y, say that x <_R y if |x| < |y| in the usual ordering, and say -x <_R x.

Anonymous

Anonymous Wed 09 Feb 2022 00:37:33 No.14203693 Report

Quoted By:

>>14203689
*arbitrary x, y
My bad

Anonymous

Anonymous Wed 09 Feb 2022 01:14:36 No.14203827 Report

Quoted By: >>14203868

>>14203494
>>14203660
>only correct answers lack replies
typical
there is no process to determine whether or not a comment contains the correct answer
nor any process to identify an authority that would serve as judge
talk about land of the blind

Anonymous

Anonymous Wed 09 Feb 2022 01:27:09 No.14203868 Report

Quoted By:

>>14203827
Well what do you want, thank you replies?

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