The lack of a zero would not limit mathematics as much as you would think.
Contrary to popular belief, it is possible to have a place-sensitive number system without any digit to represent zero. It's slightly cumbersome, but can represent any real number except zero itself.
How it works:
If you eliminate zero, you just need to introduce an additional digit to represent the number base. For example, in base ten, the digit for ten could be "X".
So, to count from one to twenty-five, you would have:
1, 2, 3, 4, 5, 6, 7, 8, 9, X, 11, 12, 13, 14, 15, 16, 17, 18, 19, 1X, 21, 22, 23, 24, 25
Note that "1X" represents twenty, even though it starts with a 1. Specifically, "1X" means you have ten ones ("X" in the ones column), and one ten ("1" in the tens column). If we grew up with this system, we would probably call this number "ten-teen" or the like.
Counting from 95 to 115 would look like this:
95, 96, 97, 98, 99, 9X, X1, X2, X3, X4, X5, X6, X7, X8, X9, XX, 111, 112, 113, 114, 115
"9X" represents one hundred ("nine tens and ten ones"), and would probably be pronounced something like "ninety-ten".
You could also use a decimal point with this system, but it's a little cumbersome, because you would have to use scientific notation for numbers less than one:
1.234567 = 1.234567
2.01 = 1.X1
0.00201 = 2.01×10-3 = 1.X1×X-3
The above examples are in base ten, but of course you can use any number base you wish.