/sci/ - Science & Math

>>12002632
>every natural number is in he neighborhood of the origin.
and? that doesnt mean they arent in the neighborhood of infinity
the ceiling function is defined for all reals, is it not? for any real in the neighborhood there are naturals even larger than it

Assuming for contradiction that there are no naturals in the neighborhood of infinity, take two elements in the neighborhood [math] a=\widehat{\infty} - 1, b=\widehat{\infty} - 10 [/math], then [math] a-b = 9 [/math]
so there are reals in the neighborhood of infinity that are more than 1 unit away from each other, and so there must be an integer between them

>>12002662
>I meant to say that it is not clopen in the long line which is the OBVIOUS relevant aspect of clopenness.
so we can agree that the Real line and the long line are different, cool
you still havent shown that the long line doesnt satisfy the conditions, pic

>I think I can begin a standard analysis by saying "Let THING be a Hausdorff space,"
Took, taking an arbitrary Hausdorff space isnt the same as defining a specific object

>Hausdorff has already defined a Hausorff space, luckily for me.
then why dont you use it?

>Indeed, I don't even need to define points at all because it suffices to invoke a Hausdorff space
Took, you cant prove things about the real numbers specifically if you only ever look at one fucking property

>You never defined the Latin alphabet in which you are crafting posts, and yet I am able to understand what you write. How is that, do you think?
stop being a nigger, you know thats unrelated to math