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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
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What is The set of all odd natural numbers less than 10 is?
The set of all odd natural numbers less than 10 is [1,3,5,7,9].
The set of all odd natural numbers less than 10?
1,3,5,7,9
What is the set of odd numbers that are less than 12?
The set of odd numbers less than 12 includes the numbers 1, 3, 5, 7, 9, and 11. Odd numbers are integers that are not divisible by 2, so they have a remainder of 1 when divided by 2. In this case, all the odd numbers less than 12 fit this criteria and form a finite set.
What is the set of odd numbers less than 19?
The set of odd numbers less than 19 includes all integers that are not divisible by 2 and are smaller than 19. These numbers are 1, 3, 5, 7, 9, 11, 13, 15, and 17. They form a finite set of numbers that are alternately spaced by a difference of 2.
Write a set representing all odd natural numbers less than 6?
1,3,5
