Infinitely many. There are, in fact, infinitely many numbers between any two numbers.
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10,000. from 0000 to 9999.
10,000 of them, from 0000 to 9999. However, most people would not count numbers with leading 0s, so that there would be 9000 4-digit numbers.
If leading zeros are allowed, then you have 0000 through 9999 which is 10,000 numbers.If leading zeros not allowed: the smallest four-digit number is 1000, eliminating 0000 through 0999 (one thousand numbers are not allowed), so it is 9,000 numbers.
Specify whether you are including the numbers between 0000 and 1000.
0000 to 9999 So answer is 10,000 as 0001 to 9,999 is 9,999 plus 0000 is a number also so 9,999 + 1 = 10,000