Determine whether the set is finite or infinite

Question

{x|x e N and x > 1000}

 

(e is the element of)

Answer 1

The set of natural numbers is infinite.  

 

The set {x|x e N and x > 1000} is equal to the natural numbers minus the finite set {x|x e N and x ≤ 1000} .

 

Therefore this new set {x|x e N and x > 1000} is infinite because the result of an infinite set minus a finite set is always still infinite.

Answer 2

Hi, Pamela!

 

The set that you described can be written as "The set of all numbers x such that x is a Natural number and is greater than or equal to 1000."  If you recall, Natural numbers are counting numbers (0, 1, 2, 3, 4, 5...).  They are non-negative integers.  Also, to answer this question, you need to know what finite or infinite sets mean.  A finite set is one with a limited number of elements that are part of the set.  An infinite set has no limit; you cannot number how many elements are in a set because the set continues on and on into "infinity."

 

Returning to the set that you asked about:  The question is asking whether there is a finite or infinite number of Natural numbers that are greater than or equal to 1000.  Let's list some: 1000, 1001, 1002, 1003,...  Does this ever stop?  No; instead, the list continues on into positive infinity.  So there is an infinite number of elements of this set.  Therefore, this is an infinite set.

 

Hope this helps!

 

Patty