N-0-1-2-N-0-I-know-that-if-S-k-0-1-2-S-N-0-Because-you-can-forever-pair-one-value-from-one-set-to-another-In-my-question-bellow-I-use-the-word-combine-

Question Number 5080 by FilupSmith last updated on 10/Apr/16

N = {0, 1, 2, \dots}

∣ N ∣ = ℵ_{0}

I know that :

if S = {k, 0, 1, 2, \dots}

∴ ∣ S ∣ = ∣ N ∣ = ℵ_{0}

Because you can forever pair one value

from one set to another .

In my question bellow I use the word

^{'} {c o m b i n e}^{'} . What I mean is something

like this :

{1, 2, 3} + {2, 3, 4} = {1, 2, 3, 2, 3, 4}

o r = {1, 2, 2, 3, 3, 4}

o r d e r {d o e s n}^{'} t m a t t e r

i a m u n s u r e h o w t o w r i t e t h i s m a t h e m a t i c a l l y c o r r e c t

My question is as follows :

If we combine ℵ_{0} lots of sets, with each

set containing ℵ_{0} values, is the total

values greater than ℵ_{0} ?

e . g .

G = N + N + \dots + N ℵ_{0} times

G = {0, 0, \dots, 1, 1, \dots, 2, 2, \dots}

Is ∣ G ∣> ℵ_{0} ?