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There are infinitely many numbers between 1032 and 1209. Let me begin to explain my answer by presenting a modified version of the original question:

"How many whole numbers are there between 1032 and 1209?"

The answer? There are 76 whole numbers between 1032 and 1209.

So, I would say there are two possibly-confusing things going on here. One of them is the distinction between "numbers" and "whole numbers"; and the other is the distinction between "the difference between two numbers" and "the number of numbers between two numbers."

"Whole numbers" are the number 0, the number 1, and any number that is the sum of the number one added to itself, however many times. So, 0, 1, 2, 3, 4, 5, and so on, are all whole numbers.

There are infinitely many whole numbers (because there's no end to the numbers you can get by adding 1 to the preceding number), but the number of whole numbers between any two, non-negative numbers (not including Infinity) is always finite. Between 2 and 5, for example, there are two whole numbers: 3 and 4. Between 2 and 1,000,005 there are 1,000,002 whole numbers, which you can name by starting with the number 3, and counting up -- by ones -- to the number 1,000,004. That's the number you would stop with because we are naming (and counting) the whole numbers between 2 and 1,000,005.

Between 1032 and 1209 there are 76 whole numbers. To get the number of whole numbers between two non-infinite, non-negative numbers, you take the difference of the two numbers (the smaller number subtracted from the larger number) and subtract 1. The difference between 2 and 5 is 3; and the number of whole numbers between 2 and 5 is 2 -- namely, 3 and 4. The difference between 1032 and 1209 is 77, and the number of whole numbers between them is 76.

But when you ask about "numbers" instead of "whole numbers" you are including the infinitely many intervening numbers between any two whole numbers. There are even infinitely many intervening numbers between 0 and 1: 0.1, 0.01, 0.001, 0.00230791502, 0.00000000000000000100000000010341010984050505326, and so on. Without the restriction to whole numbers, all the infinite divisions of the number 1 would have to be named and counted, if you wanted to say "how many numbers there are between" any two numbers starting with zero and up to any positive number other than infinity -- say, for example, between 1032 and 1209. So infinitely many numbers is how many numbers there are between 1032 and 1209.

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โˆ™ 2012-08-17 07:53:47
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Q: How many numbers are there between 1032 and 1209?
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