123456
Integers, rationals. Also all subsets of these sets eg all even numbers, all integers divided by 3.
15241383936
They are collections of some, or all, of the elements of the set. A set with n elements will have 2^n subsets.
meaning of proper subsets
Partitioning is dividing a set of things into subsets such that the union of all the subsets is the original set and the intersection of any two subsets is the null set. That is, between them, the subsets account for the whole of the original set and there are no elements in more than one subset.
123456 - 7890 = 115,566
If a set has N elements then it has 2N subsets. So you can see that a list of all subsets soon becomes a very big task. For reasonably small values of N, one way to generate all subsets is to list the binary numbers from 0 to 2N. Then, each of these represents a subset of the original set. If the nth digit is 0 then the nth element is not in the set and if the nth digit is 1 then the nth element is in the set. That will generate all the subsets.
An element doesn't have subsets. Sets can have subsets.
123456 x 17=2'098'752
There are no subsets of irrational numbers. There are subsets of rational numbers, however.
Yes all sets have subsets.Even the null set.