Question

Cardinal number

Answer 1

\[D_n=\{\langle d_k\rangle \in Q^N:d_k=0, k>n\}\] what is cardinality of this set?

Answer 2

Is it n+1 (first n coordinates from N and 0)?

Answer 3

a number denoting quantity (one, two, three, etc.), as opposed to an ordinal number

Answer 4

can you tell me what is cardinality of this set?

Answer 5

i think it is the number of subsets of a set.

Answer 6

\[cardinal no. of a set=2^{n} ,where n is the no of elements of the set.\]

Answer 7

why 2^n? I mean, why 2?

Answer 8

i give you example.
S={1}
\[Its subsets are \phi and \left\{ 1 \right\}\]
They are two in number.
now I take S={1,2}
Its subsets are
\[\phi ,\left\{ 1 \right\},\left\{ 2 \right\},\left\{ 1,2 \right\}\]
They are four in number.
\[S=\left\{ 1,2,3 \right\}\]
try and get eight numbers.

Answer 9

ok, but can you help me with the set I wrote? I have written that \[|D_n|=|Q^n|=\mathbb{N}_0^n=\mathbb{N}_0\] where \[\mathbb{N}_0\]is alef-zero