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awarded  Nice Question
Apr
21
awarded  Necromancer
Apr
21
revised Is a closed set minus its limit points open?
formatted maths
Apr
21
suggested approved edit on Is a closed set minus its limit points open?
Apr
21
revised Is a closed set minus its limit points open?
added 516 characters in body
Apr
21
awarded  Revival
Feb
11
accepted cyclic definitions of material/logical implications
Feb
2
revised Proof of inequality: If $x+y+z=0$, then $xy+yz+zx \le 0$?
replaced "is less than or equal to" with "$\le$"
Feb
1
suggested approved edit on Proof of inequality: If $x+y+z=0$, then $xy+yz+zx \le 0$?
Jan
14
comment Does maximum or supremum of an infinite set exit?
Glad you solved the problem. Don't forget to upvote and accept the answer you think is the most helpful.
Jan
14
comment Does maximum or supremum of an infinite set exit?
@Amanda for another example, take the set of all prime integers. There are countably infinitely many, and each prime integer is "finite", yet there is no maximum or supremum of the set.
Jan
14
comment Does maximum or supremum of an infinite set exit?
Yes. By the pattern, $1, 2, 3, 4, 5, \dots$, each is a natural number. Natural numbers are known to be "finite," that is, informally, "less than infinity."
Jan
14
revised Does maximum or supremum of an infinite set exit?
added 18 characters in body
Jan
14
comment Does maximum or supremum of an infinite set exit?
Agreed, but I think from anyone asking this type of question, whether the issue might have some involvement is unclear.
Jan
14
comment Does maximum or supremum of an infinite set exit?
Thanks for clarifying. You should specify this in your question so that users won't give examples such as $(a,b)$ or $[a,b]$, as each of those contains an uncountably infinite number of points.
Jan
14
comment Does maximum or supremum of an infinite set exit?
Because the OP describes $S$ as $\left\{k_1, k_2, \dots, k_n\right\}$, it seems that $S$ must contain a countably infinite number of points, thus intervals such as $[a,b]$ or $(a,b)$ are not good examples.
Jan
14
comment Does maximum or supremum of an infinite set exit?
By the way you describe $S$, it looks like you want it to have a countably infinite number of elements. Thus $S$ may not take the form of any interval, open or closed or otherwise, on the Real line. Is this correct?
Jan
14
answered Does maximum or supremum of an infinite set exit?
Jan
12
revised How to understand point functions
added 266 characters in body
Jan
12
answered How to understand point functions