all your base-10 are belong to us.

I was thinking of my usual thought process and I came across the newfangled concept that there is no such thing as an absolute fact. Everything known to be certain is really only known based on some underlying context or bias. That old chestnut. An internal conversation ensued. "What about math? Math is always consistant." "Only within consistant axioms. What's 1+1?" "Two" "Why?" "Because that's what it means to add 1 to 1." "That's what it means to you. And to anyone using the standard meanings of both "one" and "plus"" "What?" "Let's say I make my own base-10 numbering scheme except each number is mapped to the name and symbol of the following number. For example, my '4' would be your '3'. Thus, '1' + '1' = '1'. " "That's ridiculous." "Better yet, keep the numbers & symbols, and just change the base. What's 1+1 in base-2? 10." "Base-2?" "Yeah, it's where you only have digits 0 and 1. not 2 or above." "Well that's a strange name." "Why's that strange?" "Because if all you knew was base-2 then you wouldn't have a concept of the number '2' to describe the base" "Interesting" "What do you call normal math?" "Base-10" "There isn't a single digit to describe 10? You use base-10 numbers to describe the base of a base 10 number?" "I suppose." "Why don't you do that for other bases, then, what makes 10 so special?" "Fine, we'll do it for other bases as well." "Good. Now what does that make base-2?" "Base-10."