Family of Real Numbers

Discussion in 'Algebra' started by solo_guitar, Sep 12, 2024.

  1. solo_guitar

    solo_guitar

    Joined:
    Aug 22, 2024
    Messages:
    61
    Likes Received:
    4
    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.
     
    solo_guitar, Sep 12, 2024
    #1
  2. solo_guitar

    Alonzo

    Joined:
    Aug 14, 2024
    Messages:
    8
    Likes Received:
    2
    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.
     
    Alonzo, Sep 12, 2024
    #2
    solo_guitar likes this.
  3. solo_guitar

    solo_guitar

    Joined:
    Aug 22, 2024
    Messages:
    61
    Likes Received:
    4
    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.
     
    solo_guitar, Sep 12, 2024
    #3
Ask a Question

Want to reply to this thread or ask your own question?

You'll need to choose a username for the site, which only take a couple of moments (here). After that, you can post your question and our members will help you out.
Similar Threads
There are no similar threads yet.
Loading...