DescentBB

Decimal is base 10, and goes from 0 to 9
Octal is base 8, and goes from 0 to 7
Binary is base 2, and goes from 1 to 2
A tally chart is base 1, and you have as longer string as number you have
But what is base 0? Infinities?

Base 0 is singularity

Tally marks use only one symbol, but it's not clear to me that tally marks form a base 1 number system. For instance, you can represent a positive integer n in base b using ceil(log_b(n + 1)) "digits," where log_b is log base b, but log base 1 is undefined.

Binary only goes from 0 to 1, not 1 to 2.

Oops!

Yeah, oops about teh binary.
You're right about the tally chart, you need some number to tell how long it is.