devans99 wrote: ↑Tue Nov 27, 2018 1:56 pm
lim x->∞ (2/x) ~= lim x->∞ (1/x)

Both expressions tend to zero as x tends to infinity. But at no point on the way to infinity are the two expressions equal. So we write approximately equal.

We can also write

2/x > 1/x for all x except 0.

So maybe its best to write:

lim x->∞ (2/x) >~ lim x->∞ (1/x)

So '>~' denotes its approximately equal with 1/x always being less than 2/x.

Sorry. No can do. This is special pleading.

lim x->∞ (2/x) lies on the real number line, does it not?

lim x->∞ (1/x) lies on the real number line, does it not?

A = B

A < B

A > B

Can ALWAYS be determined for any two real numbers, and since we never actually evaluate AT infinity itself then I will settle for nothing less than:

lim x->∞ (2/x) > lim x->∞ (1/x) for x > 0

lim x->∞ (2/x) < lim x->∞ (1/x) for x < 0