Let A = { -6, - 12/4 , - 5/8 , - √3, 0, 1/4 , 1, 2π, 3, √12}. ...

Question

Let A = { -6, - 12/4 , - 5/8 , - √3, 0, 1/4 , 1, 2π, 3, √12}. List all the elements of A that belong to each set. Natural numbers

Accepted Answer

Hello. Everyone in this video we're going to be looking at this practice problem where we want to identify the natural numbers in C. M which includes negative 1028 negative 2050 divided by five. Negative three divided by 25. 04 divided by 21 1 Radical 24 and nine pi. So in order to identify the natural numbers, let's remember what a natural number is. So a natural number is The counting numbers starting from one all the way to infinity. So counting numbers is 123-4567. So notice how there's no decimals or fractions in the natural counting numbers and notice how the natural counting numbers start at one. Which means that we need to exclude any number Less than one. So that includes Negative numbers or zero. And like I said before we're not counting decimals or fractions. So we can exclude decimals and fractions. So now that we've sort of set up the rules we can go ahead and start eliminating or finding the natural numbers and set em so the first three numbers are negative which means that I can eliminate those right away because I know that they're not natural numbers. And then I have zero. And we've already established that zero is not part of the natural number realm since we have to start out one. So I can't include zero. Then I have four divided by 21. So four divided by 21 is actually less than one. Since one in this fractional form would be 21/21. So because it's less than one, I can also exclude it from my set of natural numbers and then I have one. So one is where my natural numbers begin so I can go ahead and start my list where I list the natural numbers And I'll write one And then I have radical 24. So if I look at radical 24 and I try to simplify it I can write it as radical four times radical six and I can simplify radical force since I'm looking for the square root before and I know that's too so I'll have two times Radical six. And because Radical six is a decimal I can't include it in the natural numbers list. So I can exclude Radical 24 and then I have 11 and 11 is not a decimal and it's greater than one and it's one of the natural counting numbers. I can go 9 10, 11, 12. So I can include it in my natural numbers list. And lastly I have nine pi so nine pi has pie which is a never ending decimal. And because nine times pi has this never ending decimal, I can't include it in my set of natural numbers. So nine times pi also gets excluded And you can see down here that my set of natural numbers is just one and and you can see that that aligns with answer choice B So hopefully this video helped and see you next time

Let A = { -6, - 12/4 , - 5/8 , - √3, 0, 1/4 , 1, 2π, 3, √12}. List all the elements of A that belong to each set. Natural numbers

Key Concepts

Set Theory and Membership

Natural Numbers

Number Types and Classification

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