The smallest four-digit number not using zero is 1000. In a four-digit number, the first digit cannot be zero, so the smallest possible value for the first digit is 1. The remaining three digits can be any number from 0-9, so the smallest possible four-digit number is 1000.
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That would be the same as the smallest four-digit even number: 1,000, which also happens to be the smallest four-digit whole number.
The smallest four digit number is 1000. It is even so 1001 is the smallest four digit number that is odd.
If you allow non integers, then your smallest four-digit number would be .0001. If you only allow integers, then your smallest four-digit number would be 1000. Your largest four-digit number would be 9999.
2034
Provided that the first digit cannot be 0, 1000 is the smallest number with four digits. Otherwise there are smaller numbers with 0 to thousandth digit such as 0100, 0050. The smallest integer in such instance is 0000.