<p>This is a problem from "Real SAT subject test". Can someone please help me?? ><</p>
<p>Which of the following has an element that is less than any other element in that set?</p>
<p>I. The set of positive rational numbers
II. The set of positive rational numbers r such that r^2>=2
III. The set of positive rational numbers r such that r^2>4</p>
<p>a) none
b) I only
c) II only
d) III only
e) I and III</p>
<p>I chose b but the answer is a. This is what I thought: for any rational number n/m (m>0, n>0) , (n)/(m+1) will always be smaller than n/m, and therefore you can't find a smallest one. </p>
<p>I don't know... This is confusing!! :(</p>
<p>No idea... I would've said b, too.</p>
<p>The set of positive rational numbers can't be correct because you can't pick 0, and anything you pick can be even smaller yet than what you picked. On II and III, you can have negatives which throws them off. Therefore, like you said, the answer has to be a.</p>
<p>EDIT: So what you said does make sense and is the reason...</p>
<p>Exactly, You cant really FIND the SMALLEST number in dealing with rational numbers (unless you have 0 which u dont), Because there are INFINITE Rational Numbers Between Any two Integers So between 0 and 1, there are Infinite number, so you cannot possibly find the smallest number, as for the other choices, its basically the same thing, just with a higher number restriction, same rules apply, thus the answer has to be a</p>
<p>I think this problem had a lot of potential but was ultimately too easy. I like this alternative (correct answer [D]) better:</p>
<p>Which of the following has an element that is less than any other element in that set?</p>
<p>I. The set of positive irrational numbers
II. The set of positive rational numbers r such that r^2>=2
III. The set of positive rational numbers r such that r^2>=4</p>
<p>a) none
b) I only
c) II only
d) III only
e) I and III</p>
<p>oh! I get it. I don't know what I was thinking. :) must be out of my mind... hope this won't happen next satursday...</p>
<p>Ohh, I get that one, octalc0de.</p>
<p>Which of the following has an element that is less than any other element in that set?</p>
<p>I. The set of positive rational numbers
II. The set of positive rational numbers r such that r^2>=2
III. The set of positive rational numbers r such that r^2>4</p>
<p>a) none
b) I only
c) II only
d) III only
e) I and III</p>
<p>I'm pretty positive this is the explanation for why it's A none:</p>
<p>The question asks " Which of the following has an element that is less than any other element in that set?" (So obviously this question has to do with a definitive Lower bound right?)
I. The set of positive rational numbers
Allright Positive rational numbers- this means the number has to be greater than zero- it can be expressed as 1/x where x is a rational number and is ever increasing thus the lower bound is indefinite and there is no element that is truly lower than every single other element. </p>
<p>II. The set of positive rational numbers r such that r^2>=2
Allright basically the same thing here, if R Squared equals or exceeds 2 than R equals or exceeds root 2. Notice that Root 2 is not a rational number and thus the same situation occurs again, a number ever decreasing with root 2 as the asymptote (it's irrational and thus it's not in the solution set. So there is no definite lower bound.</p>
<p>III. The set of positive rational numbers r such that r^2>4
Pretty much the same exact thing- r has to be greater than 2 with and the same thing happens a small amount can always be smaller when added to the LB of 2.</p>
<p>Anyways that's the way I saw it. =p</p>