Results 1 to 3 of 3

Thread: more set theory questions

  1. #1
    Senior Member
    Joined
    Mar 2017
    From
    Toronto
    Posts
    295
    Thanks
    2

    Question more set theory questions

    Hi,


    I hope someone can help me tease out the logic in these in order to determine whether they are true or false.


    1) {2s+1|s∈ℝ}=ℝ
    I would think that this would be true since any real number for "s" would result in 2s + 1 equating to a real number. Is this right to think?


    2) ℕ ⋂ ℕ = ℕ
    Essentially this statement is saying that the intersection of the natural numbers with the natural numbers, is the natural numbers - therefore, I believe that this statement is true.


    Let me know what you think!
    - Olivia
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    21,494
    Thanks
    2730
    Awards
    1

    Re: more set theory questions

    Quote Originally Posted by otownsend View Post
    1) {2s+1|s∈ℝ}=ℝ
    I would think that this would be true since any real number for "s" would result in 2s + 1 equating to a real number. Is this right to think?
    2) ℕ ⋂ ℕ = ℕ
    1) If $s\in\mathbb{R}$ then $2s+1\in\mathbb{R}$.
    Now say that $x\in\mathbb{R}$. Then if $s=\frac{x-1}{2}$ then $s\in\mathbb{R}$
    Is it true that $2s+1=(x-1)+1=x~?$
    How does that prove #1?

    #2 is just a stupid question. Whoever set the question should be fired.

    On the collection of sets, $\forall A:~A\cap B\subseteq A$
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Aug 2017
    From
    Finland
    Posts
    34
    Thanks
    10

    Re: more set theory questions

    otownsend, your explanations are correct imo.
    Plato, though #2 send to be lame, it is an important result in set theory. Trust me, many get confused and struggle with it doubting whether how can that be such simple.

    .
    ..
    ...
    Be patient, TEX will load, eventually...
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. A few set theory questions
    Posted in the Discrete Math Forum
    Replies: 7
    Last Post: Aug 7th 2012, 03:39 PM
  2. Two set theory questions
    Posted in the Discrete Math Forum
    Replies: 5
    Last Post: Feb 9th 2010, 12:47 PM
  3. Questions on set theory
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: Jan 16th 2010, 09:19 PM
  4. Set theory questions
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: Sep 27th 2009, 04:15 PM
  5. Theory questions
    Posted in the Business Math Forum
    Replies: 1
    Last Post: Sep 28th 2006, 07:46 PM

Search Tags


/mathhelpforum @mathhelpforum