Real values close to 10

[eranga262154]

Say I have a set, denoted by A, which represent values(real numbers) close to 10. How can I represent it using the way of set representations.

[jemidiah]

After a brief search on "set representation" I didn't really find anything that explains this concept. Maybe you just mean set notation?

[eranga262154]

Even on set notation is fine, I'll work it on set representation later.

[jemidiah]

I'm not very confident that I understand the question, but... I'll give it a shot.

Let e and d be arbitrarily small numbers (e stands for epsilon, d for delta; like in epsilon-delta). Then the set S₁₀ (the set of real values close to 10) is {x| abs(x-e) <= d} [x belongs to the reals]

Again I'm not sure that this is what you want but S₁₀ is a set of real values that are close to 10....


If this wasn't what you wanted, could you provide an example? Perhaps then we could be on the same page.

[eranga262154]

{x| abs(x-e) <= d} [x belongs to the reals]

Even what I know about sets, I believe this is correct. But I found one explanation like this,

1 + (X - 10²)^(-1) where, X belongs to the reals.


I'm confusing with it, have you any comments.

[jemidiah]

That function you've listed confuses me too if it's supposed to connect to real values close to 10.

Depending on the X you choose, that function evaluates to anything (it's invertible except for X = 100). Here's some values I plugged in to get a feel for the function:

1 + (X - 100)^(-1) = f(X)

f(-1000) = ~0.999
f(-100) = 0.995
f(-10) = ~0.991
f(-1) = ~0.990
f(0) = 0.99
f(1) = ~0.990
f(10) = ~0.989
f(90) = 0.9
f(98) = 0.5
f(99) = 0
f(99.5) = -1
f(99.75) = -3
f(99.9999) = ~-10,000
f(100) = [undefined]
f(100.0001) = ~10,001
f(100.5) = 3
f(101) = 2
f(110) = 1.1
f(1000) = ~1.00

For most inputs of X it gives values very near 1; maybe that's the part that's supposed to help answer this question?

In any case I'm still confused by that function.

[eranga262154]

Actually I checked that function as you done. But still confusing. Anyway, you are same that what I thought. Thanks.