# Are there more integers then whole numbers?

4 posts

 This is a interesting mathematical paradox I recently noticed. Ones first reflex should, theorically, be to say "yes", as, after all, whole numbers include natural numbers, plus also negative whole numbers. The thing is that, for you to be able to say there are more integers then whole numbers, first, you would need to say there is a set amount of whole numbers and a set amount of natural numbers. This is not the case. In both cases, the value is infinite. If you are to try to count how many whole numbers and how many integers are there, no matter how much time you were given or how fast you were counting, the counting would simply never end. See, the thing about infinity is that it is not a number: It is a concept. It is to designate something without limit or end, something which can therefore never be counted or numbered. Let me put it this way: If I could lift a infinite amount of weight, it would be impossible for anyone to be able to lift more then me, as if that were the case, then there would be a amount of weight which I cannot lift, and if there is a amount of weight that I cannot lift, therefore I cannot lift a infinite amount of weight. So, thoughts? Answer: No. There are exactly the same number of integers and whole numbers. That size is called aleph-zero. For further study, learn about Cardinality https://en.wikipedia.org/wiki/Aleph_number. > *Originally posted by **[Jp_Ragavan](/forums/9/topics/1662395?page=1#13076707)**:* > The Answer is yes... > Even if you assume there are infinite (n) whole numbers [including zero] in the positive side, there are a total of (2n) Integers. > Dont get confused by the term infinite. > Remember in math, limits from minus infinity to plus infinity can be written as 2(limit from 0 to infinity)... which means the negative numbers also matter... So there would be roughly 2x Integers than whole numbers You just got confused by this term yourself. ∞ and 2 x ∞ are exactly the same. Just like 0 and 2 x 0 are the same. In math terms the two are the same. Integer and 'whole number' are interchangable terms for the same thing. Ragavan, I suspect you're getting *natural number* and *whole number* confused. The two terms mean quite different things. Natural number being a subset of whole number, including only those that are greater than zero. Negative whole numbers are simply defined as real integers that are less than zero, and vice versa. *Note. I say 'in math terms', because the various computing fields do define integers a little differently. They have limits for practicality's sake.