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 September 8th, 2013, 06:34 AM #1 Newbie   Joined: Jun 2012 Posts: 17 Thanks: 0 How to define the set of all primes? I started studying mathematics a week ago and for a homework assignment we have to define the set of all primes. Is this correct? {x element of N : for all y((y element of N) and (y =/= 1) and (x>1)) -> ((x/y) is not an element of N)) Or is there an easier method? Etham,
 September 8th, 2013, 07:11 AM #2 Senior Member   Joined: Jun 2013 From: London, England Posts: 1,316 Thanks: 116 Re: How to define the set of all primes? What you've done is excellent, although you could tidy it up a bit. For example: $\lbrace x\in \mathbb{N}:\ x=> 1; \ and \ for \ y\in \mathbb{N}, \ y/x \Rightarrow y= 1 \ or \ y = x \rbrace$ Note that by definition 1 is not prime, although it meets the main criteria. $y/x$ means "y divides x" and is equivalent to $\frac{x}{y} \in \mathbb{N}$ and is the more usual way to express this. Formal definitions like this are not easy, but your attempt shows that you really understand what you are trying to do.
 September 8th, 2013, 07:22 AM #3 Newbie   Joined: Jun 2012 Posts: 17 Thanks: 0 Re: How to define the set of all primes? Haha, Thanks! I feel stupid for not thinking of just saying y = 1 or y = x. Your set makes alot of sense. Thank you!
 September 8th, 2013, 07:40 AM #4 Newbie   Joined: Jun 2012 Posts: 17 Thanks: 0 Re: How to define the set of all primes? In your set can I change the 'and for' into 'for all' you know the A but then rotated 180 degrees?
September 8th, 2013, 08:52 AM   #5
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Re: How to define the set of all primes?

Quote:
 Originally Posted by etham In your set can I change the 'and for' into 'for all' you know the A but then rotated 180 degrees?
It's not necessary, although it's probably not wrong. In this case, the fact that it is for any y is implicit in the condition.

September 9th, 2013, 04:06 PM   #6
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Re: How to define the set of all primes?

Quote:
 Originally Posted by etham I started studying mathematics a week ago and for a homework assignment we have to define the set of all primes. Is this correct? {x element of N : for all y((y element of N) and (y =/= 1) and (x>1)) -> ((x/y) is not an element of N))
No, this is NOT quite correct. For example, x= 17 is prime but x/y is an element of N if y= 17.

Quote:
 Or is there an easier method? Etham,

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