Understanding Sets and Natural Numbers

The video tutorial explores finding the smallest element in various sets defined by mathematical conditions. It begins by defining natural numbers and then analyzes four different sets, each with unique conditions. The tutorial demonstrates how to determine the least element in each set by testing values and applying logical reasoning.

What is the definition of natural numbers used in this context?

• Natural numbers start from 1.

• Natural numbers are only odd numbers.

• Natural numbers are only even numbers.

• Natural numbers include 0, 1, 2, 3, and so on.

In the first set, what is the smallest natural number n such that n squared plus 4 is greater than or equal to 10?

• n = 3

• n = 1

• n = 0

• n = 2

Why is n = 0 not included in the first set?

• Because 0 squared plus 4 is less than 10.

• Because 0 squared plus 4 is greater than 10.

• Because 0 is not a natural number.

• Because 0 squared plus 4 is equal to 10.

For the second set, what is the smallest natural number n such that n squared minus 3 is also a natural number?

• n = 0

• n = 1

• n = 2

• n = 3

Why is n = 1 not included in the second set?

• Because 1 is not a natural number.

• Because 1 squared minus 3 is greater than 0.

• Because 1 squared minus 3 is not a natural number.

• Because 1 squared minus 3 is equal to 0.

In the third set, what is the smallest value of n squared minus 4?

• 0

• -4

• 4

• 2

Why is the smallest element in the third set negative four?

• Because n squared minus 4 equals two when n is zero.

• Because n squared minus 4 equals four when n is zero.

• Because n squared minus 4 equals negative four when n is zero.

• Because n squared minus 4 equals zero when n is zero.

In the fourth set, what is the smallest natural number n such that n equals k squared minus 2?

• n = 1

• n = 2

• n = 0

• n = 3

Why does k = 0 not work in the fourth set?

• Because k squared minus 2 is less than 0.

• Because k squared minus 2 is equal to 0.

• Because k squared minus 2 is greater than 0.

• Because k squared minus 2 is not a natural number.

What is the relationship between n and k in the fourth set?

• n equals k squared plus 2

• n equals k squared divided by 2

• n equals k squared minus 2

• n equals k squared times 2