Identify each set as finite or infinite. Then determine whethe...

Question

Identify each set as finite or infinite. Then determine whether 10 is an element of the set. {1, 1/2, 1/4, 1/8, ....}

Accepted Answer

Welcome back. I am so glad you're here. We are Given this set. 1 1/6 1 36th one, 216th. And ellipses were asked to determine whether the set is finite. Whether it has an end or is infinite, it goes on forever. And also to check to see if six belongs to this set. All right. Well, with finite versus infinite, that one's pretty quick to answer because the ellipses at the end of our set indicate that this is going to go on for absolutely forever. So, this is in fact an infinite set. All right. How about if six belongs to this set? Well, you can tell intuitively that these numbers they are getting smaller and smaller and smaller, their fractions after the one. And so no, it's not going to suddenly go up to six. How could we enumerate what's going on? The pattern? That's happening here to prove to ourselves that six cannot belong. Well, that one that is the same actually as 1/6 to the zero power because six to the zero, anything raised to the zero is actually equivalent to one. So, that's how we get one for the first number in our set. The second one is 1/6 to the first. The third one is 1/6 squared. The third one is 1/6 to the third. The fourth, one is 1/6 to the third And then it's going to keep going in that pattern where the exponents of the six in the denominator. We'll just keep getting bigger but we're never going to reach the whole number six, so that's how we know that no six cannot belong to this set. Alright. We look at our answer choices infinite six, nope doesn't belong, and this matches with answer choice. D. Well done. We'll catch you on the next one.

Identify each set as finite or infinite. Then determine whether 10 is an element of the set. {1, 1/2, 1/4, 1/8, ....}

Key Concepts

Finite vs. Infinite Sets

Set Notation and Elements

Membership in a Set

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