Family of Real Numbers

[solo_guitar]

It is important to classify the different kinds of numbers that we deal with everyday.

Let R = set of real numbers.

R = {counting or natural numbers, whole numbers, rational numbers, irrational numbers, and integers}

Assignment

Make two lists of two kinds of numbers listed in set R.

I will do the first list.

Counting or Natural: 4 and 10

Whole: 0 and 8

Rational: 4/3, 0.12

Irrational: sqrt{2}, pi

Integers: -45, 60

Now, it's your turn.

 

[Alonzo]

You can also include the algebraic numbers, those which are solutions to polynomial equations with rational coefficients. E.g., sqrt(2) is irrational (easy reductio ad absurdum proof), but it is algebraic, solution to x^2-2=0.
Pi and e are not algebraic (tougher proof, I do not know it) - these numbers are called transcendental.

 

[solo_guitar]

You can also include the algebraic numbers, those which are solutions to polynomial equations with rational coefficients. E.g., sqrt(2) is irrational (easy reductio ad absurdum proof), but it is algebraic, solution to x^2-2=0.
Pi and e are not algebraic (tougher proof, I do not know it) - these numbers are called transcendental.

True but let's keep things simple for now. My threads will get increasingly challenging as the weeks and months go by. Let's stay away from transcendental numbers for now.