Re: how

Le 12/04/2024 à 17:51, Tom Bola a écrit :

WM schrieb:
 

Le 12/04/2024 à 17:00, Tom Bola a écrit :

WM schrieb:
 

Le 12/04/2024 à 16:40, Tom Bola a écrit :

WM schrieb:
 

Le 12/04/2024 à 15:56, Tom Bola a écrit :

WM schrieb:

 

Consider the set {1, 2, 3, ..., ω} and multiply every element by 2 with the result {2, 4, 6, ..., ω*2}. What elements fall between ω and ω*2?

 {w+1, w+2, w+3, ...}

 No, all elements emergeing from doubling have larger distances than 1.

 

What size has the interval between N*2 and ω*2?

 N*2 is not a number, so there is no interval between it and w*2

 N*2 is a set having elements but not including w*2. So there is a distance.

 This is wrong because there is a distance to any element of that set. But you probably are meaning the distance between the set limit of IN which is w and w*2

 I am meaning the distance between N*2 and ω*2 after multiplication.

 Yes, that is the set after multiplication: {0, 2, 4, 6, ..., w, w+1, w+2, w+3, ..., w*2}

 Why are the distances below ω 2 but beyond ω 1?

 This is the union of the image from IN under f(n)=2n and the "elements fall between ω and ω*2" that you wanted above

I wanted the image of 1, 2, 3, ..., ω under multiplication by 2.

 The image of IN under f(n)=2n and w is still {0, 2, 4, 6, ..., w*2}

Yes, but where is ω in this sequence?
Regards, WM