how do you show that Z is a proper subset of A?

Question

in other words, show that Z is a subset of A and that Z is not equal to A

Let A = (X element R | x,x^2,x^3....} intersecting Z not equal to empty set

it says that x is an element of R and then x,x^2,x^3...intersects the integers

and by R its reals , i guess you only take the integers in the set of real numbers??

also would 5 be an element of A, would 1/2 be an element of A??

Answer 1

A is a subset of Z. Z is not a subset of A.

See my addition to your other question about 1/2 and 5 being in the set.

Answer 2

Like the first poster said, show everything in Z is in A and something in A is not in Z.

Perhaps you should clarify the question. By Z do you mean the integers? and by R the reals? Your condition doesn't really make sense. You could mean, given some real number x construct the set {x,x^2,x^3,x^4...}. This set will not contain the integers as a subset. Or you could mean what you wrote: the set of real numbers x such that "x,x^2,x^3,..." but the 'condition' is always true because it does not assert anything, so then A would be the set of all real numbers. It is certianly true that the integers are a subset of all real numbers and that there is a real number which is not an integer.

please clarify...............

Still unclear. I don't want to seem too rude, but perhaps you should first learn the basic definitions, and how to write things mathematically, before asking questions like this. Either that or re-word the question verbally.

Additional Details

1 day ago
it says that x is an element of R and then x,x^2,x^3...intersects the integers.......no, actually it does NOT say this. What is says is "the set A is the set of all real numbers x such that x,x^2,x^3..." That's like saying "the set of all real numbers x such that Wednesday"

1 day ago
and by R its reals , i guess you only take the integers in the set of real numbers?? .......... No, you can take any set you want (almost, with limitations for first predicate logic and stuff like that). You decide what set you want to work on, then describe it clearly here and soemone might give you help with your concepts. Again, I suggest you re-word the question in plain language and then, once you get the concepts down, try to write it in formal math syntax.

23 hours ago
also would 5 be an element of A, would 1/2 be an element of A??....The way you wrote it, A is the set of all real numbers. If that is what you mean, (A is the set of all real numbers, because that is what you wrote) then I can give you an unconditional "YES": 5 is a real number and so in your set A, 1/2 is a real number and therefore in your set A.

Answer 3

First show that if x is an element of Z, then it is an element of A. This shows that Z is a subset of A.

Then show that A is not necessarily a subset of Z, by showing that there can be some element that is in A, but not in Z.

This will show that Z is a subset of A, but Z is not equal to A.