I get that. I was more talking this point: "its basis is in counting which everyone in the world does the same".
That statement isn't true. People don't do it the same way. And ours was preceded by other systems. Such as tally marks, Latin numerals etc. There ARE different ways to count things. But just like language, they can all be translated.
No it doesn't. Number 2 is a very specific numeral. And it's not found in base-2. There is no number 2. 2 TRANSLATES as 10. And before we had these numerals, there weren't even 1 or 0 for that matter. These are very specific characters. They aren't math itself.
Also: Math is MUCH more than just counting. It is however the root of arithmetic. But again, math is more than just arithmetic.
From
10 Rules for Writing Numbers and Numerals
"what is the difference between a number and a numeral? A number is an abstract concept while a numeral is a symbol used to express that number. “Three,” “3” and “III” are all symbols used to express the same number (or the concept of “threeness”)."
[My apologies to the thread for continuing with this off-topic mathematical subthread. Hopefully the following will be interesting enough to justify posting it anyway.]
Did you know that you can count without using any numbers? Suppose that you are a rancher, and take a herd of cattle from an enclosure to graze. As each individual animal leaves the barn or corral or whatever, drop a stone in a sack. Later that evening, when returning them to their starting place, remove a stone for each animal that goes back in. If you run out of stones as the last member of the herd returns, they're all there, even though you don't know how many that is. And if you have stones left in the bag, you lost some cattle. If it's one or two, you can have a quantitative sense of the number of missing cattle, but beyond a certain threshold, all you know is that you've lost a lot of them.
This is called 1:1 ("1-to-1") correspondence, the most primitive form of counting. It's also the basis for Cantor's work on infinity, and generates some fascinating paradoxes. Are there more natural numbers or more even natural numbers? The natural numbers are 1,2,3,4,5,6 ... and the even natural numbers 2,4,6,...
Intuition tells us that the first set is twice as large as the second. But both are infinite. Can one infinite set be larger (have greater cardinality in mathematical parlance) than another?
It turns out that that can happen - one infinite set has greater cardinality than another - but not in this case. We can demonstrate this as Cantor did with 1:1 correspondence. We can pair each element in the first set with a unique element in the second set:
1. 2
2. 4
3. 6
etc.
The cardinality (count) of the two sets is equal just as it was with the stones and cattle. And once again, we don't have a count. There is no number for the cardinality of an infinite set, just a name (aleph-0 in this case). There is a larger infinite set that cannot be put into 1:1 correspondence (or any other ratio of rational numbers) with the natural numbers, the real numbers. The cardinality of that set exceeds aleph-0
If you enjoy these kinds of matters, take a peak at what is called Hilbert's Hotel at
Hilbert's paradox of the Grand Hotel - Wikipedia :
"Hilbert's paradox of the Grand Hotel, or simply Hilbert's Hotel, is a thought experiment which illustrates a counterintuitive property of infinite sets. It is demonstrated that a fully occupied hotel with infinitely many rooms may still accommodate additional guests, even infinitely many of them, and that this process may be repeated infinitely often. The idea was introduced by David Hilbert in a 1924 lecture"