Identify each set as finite or infinite. Then determine whether 1...

Question

Identify each set as finite or infinite. Then determine whether 10 is an element of the set. {x | x is a fraction between 8 and 9}

Accepted Answer

Welcome back. I am so glad you're here. We are told that the set of all elements X. Such that X. Is a fraction between 13 and 14 is our set were to determine whether this set is finite, whether it has an end or is infinite, it never ends. And also to check whether 15 belongs to that set. Okay, so what is our set? Well, we're talking about numbers in between 13 And 14. All the fractions in between there. So our set is what's in here. We need to figure out if that is finite or infinite. So let's enumerate what some of that is going to be. We can write the numbers that are fractions in between 13 and 14. We can write them some of them as mixed numbers. So I'm going to demonstrate, let's just write 13.5. We know that we can convert this mixed number to an improper fraction. So it would fit our criteria of being a fraction between 13 and 14. 13 times two is 26 plus one is 27. So 27 halves is the same thing as 13.5. But I'm going to write it as 13.5 as a mixed number so that it's a little bit easier to conceptualize what I'm talking about here. So we know that 13.5 is one of those fractions in there. We know that 13 and a third would be one of those fractions in there. This isn't in order exactly. Um it's not all of them. So 13 and 1/4 would be another fraction in their 13 and 1/5. See look we can have our denominators just keep growing and growing and growing until we have 13 over. I don't know one ba jillion million googleplex. I don't know the numbers in our denominator can get infinitely huge. And because they can go on for infinity, this set here is in fact infinite. Who would have thunk that in between 13 and 14? There are infinite amount of numbers. But it's true. Now the next question is does 15 belong to this set? No 15 comes after 1415. Sorry, you do not belong here. So we look at our answer choices and this matches with answer choice. D. Well done. We'll catch you on the next one.

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Identify each set as finite or infinite. Then determine whether 10 is an element of the set. {x | x is a fraction between 8 and 9}

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