# Thread: more set theory questions

1. ## 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

2. ## Re: more set theory questions

Originally Posted by otownsend
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, $\forall A:~A\cap B\subseteq A$

3. ## 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.

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