0 and 1 are characters. The language of integers has an ordered 10 character alphabet. This is not unique among languages because it is a useful construct.
Similarly we could have said b < a is true but then it would always be true and a < b would be false and the world would be exactly the same because this is all a made up convention for the benefit of humans.
You're confusing numerals with numbers. Numerals are what we write down "0" and "1" are numerals - just marks on a sheet of paper or phospor until interpreted by the human mind.
Similarly we could have said b < a is true but then it would always be true and a < b would be false and the world would be exactly the same because this is all a made up convention for the benefit of humans.