We do too use infinity as a word, but in most math contexts
its meaning is better proscribed.

Check out the name G.Cantor to learn about different degrees of infinity.

A[sub]0[/sub] = Aleph-null = the infinity of the natural numbers

C = "the continuum" = the infinity of the reals

F = "the functionspace" = the infinity of the reals to reals functions.

Bring your questions to us.

[QUOTE=davar55;248604]We do too use infinity as a word, but in most math contexts
its meaning is better proscribed.

Check out the name G.Cantor to learn about different degrees of infinity.

A[sub]0[/sub] = Aleph-null = the infinity of the natural numbers

C = "the continuum" = the infinity of the reals

F = "the functionspace" = the infinity of the reals to reals functions.

Bring your questions to us.[/QUOTE]

SM88 doesn't have a hope in hell of understanding these concepts.

[QUOTE=science_man_88;248524]I know this is already known but the reason I can't extend it to infinity is solely based on a fact I should well know and that's [TEX]\infty +\infty = \infty[/TEX] from that fact (which I admit i saw in the text and didn't think about) we can see that [TEX]#(A union A) = 2*#A - #(A intersect A) = \infty - \infty = {undeterminable}[/TEX] I see the reason using the previously mentioned fact this is based on that [TEX]\infty-\infty = {undeterminable}[/TEX] because according to the logic [TEX]\infty + \infty = \infty[/TEX] one could claim [TEX]\infty-\infty = \infty[/TEX] or based of the example [TEX]x-x=0[/TEX] claim[TEX]\infty-\infty = 0[/TEX] or based on [TEX]x - \infty = -\infty[/TEX] which I thought I saw in the text[TEX] \infty - \infty = -\infty[/TEX][/QUOTE]

There's a reason I specified <i>finite</i> sets. Don't try to do arithmetic with infinity. You don't know enough.

[QUOTE=Mr. P-1;248670]SM88 doesn't have a hope in hell of understanding these concepts.[/QUOTE]Yet.

Give him time and a lot more tuition and there's a fair chance he will get there. Most people don't understand these concepts until undergraduate level.

Paul

[QUOTE=Mr. P-1;248670]SM88 doesn't have a hope in hell of understanding these concepts.[/QUOTE]

you know I'm not the first person lol [URL="http://tabs.ultimate-guitar.com/a/aaron_pritchett/lucky_for_me_crd.htm"]http://tabs.ultimate-guitar.com/a/aaron_pritchett/lucky_for_me_crd.htm[/URL]

but anyways, yeah I just couldn't think of a finite set that I understood all of them with I think. I'll think about it.

[QUOTE=Mr. P-1;248351]I actually meant De Morgan's laws as they apply to sets.[/QUOTE]

[url]http://en.wikipedia.org/wiki/De_Morgan's_laws#Using_sets[/url] you mean these ?

[QUOTE=Mr. P-1;248672]There's a reason I specified <i>finite</i> sets. Don't try to do arithmetic with infinity. You don't know enough.[/QUOTE]

Infinity is NOT a real number. It does not obey the axioms of a field.

two infinite in comparison ... can generate [B]any[/B]
result

[QUOTE=R.D. Silverman;248722]Infinity is NOT a real number. It does not obey the axioms of a field.[/QUOTE]

What does this mean?

The same is true of the number 2011.

Alone, it doesn't obey the axioms of a field.

[QUOTE=R.D. Silverman;248722]Infinity is NOT a real number. It does not obey the axioms of a field.[/QUOTE]

Is this remark directed at me or at SM88? I'm well aware that infinity isn't a real number. This is irrelevant because the context of my remark (and SM88's nonsensical manipulations) was cardinal arithmetic.

[QUOTE=science_man_88;248715][url]http://en.wikipedia.org/wiki/De_Morgan's_laws#Using_sets[/url] you mean these ?[/QUOTE]

Yes.