In the ordinary sense, yes. In the sense of set theory, no. –
Bernard
May 27 '17 at 23:1
Infinite sets behave differently than finite sets. Consider the map f:N→O where O is the set of all odd numbers. This can be written as a bijection f(n)=2n−1 and they have the same cardinality (|N|=|O|) –
Dando18
May 27 '17 at 23:2
Also a question to think about: if two sets are infinite, than how is one larger than the other? What constitutes their size? This is why we look at the density and countability of sets. –
Dando18
May 27 '17 at 23:2
Take the integers and the even integers (since they are a group and subgroup whereas the odds are not). If you defined "larger" to mean index bigger tha, then Z would be larger, [Z:2Z]=2, but in terms of cardinality both sets are the same size. They can be put in 1-1 correspondence with each other. –
sharding4
1 3 5 7 9 11 13
43
you
11
1,3,5,7,9,11,13
11
The set of all odd natural numbers less than 10 is [1,3,5,7,9].
19
1,3,5,7,9
1,3,5
x/x g < 18
The set of all odd natural numbers less than 10 is [1,3,5,7,9].
19
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1,3,5,7,9
1, 3, 5
1,3,5
odd numbers greater than 1 but less than 5.
The set of positive odd integers.
A set of numbers usually refers to a group (set) of numbers with certain discreption or properties. All odd numbers less than 10 is the set {1,3,5,7,9} The set of numbers which solve the problem 3x^2 -7 = 68 is {5 and -5}
Prime and odd numbers
x/x g < 18
the set of whole numbers less than 0