a and b are bounded non-empty subsets of r. for inf(a) to be less than or equal to inf(b), which of the following conditions must be met?
a) for every b in b and epsilon > 0, there exists a in a, such that a < b + epsilon.
b) there exists a in a, and b in b such that a < b.
if neither of these conditions are appropriate, what would be appropriate conditions for inf(a) to be less than or equal to inf(b)?

a) must be met

Step-by-step explanation:

We have two conditions:

a) For every and , there exists , such that .

b) There exists and such that  .

We will prove that conditon a) is equivalent to

If a) is not satisfied, then it would exist and such that, for every , . This implies that is a lower bound for A and in consequence

Then, implies a).

If is not satisfied then, and in consequence exists such that . Then and, for every ,

.

So, a) is not satisfied.

In conclusion, a) is equivalent to

Finally, observe that condition b) is not an appropiate condition to determine if or not. For example:

okay wait before i answer, is this for your points on a graph?

step-by-step explanation:

you divide the denominator by the numerator on both sides and if the quotients are equal then the fractions are equivalent