I get what you're saying but my point still applies. Did we discover the decimal form of representation out of all possible forms of representing fractional qu

I get what you're saying but my point still applies. Did we discover the decimal form of representation out of all possible forms of representing fractional quantities or did we create that form? Was the english language discovered out of the set of all possible languages or was it created? It's good to examine the intuitive differences though. Why does the choice of representation feel more "creative" than say the "choice" of what axioms to use in a certain field in mathematics? Many times you will discover that the intuition is just a biased flaw in the way we think, but many times you will discover that your intuition is demarcating an actual difference. I think our intuition is marking an actual difference here. The set of all symbols representing the number 3 is infinite not bounded by any rules. The set of all sets of axioms we can use to formulate a mathematical theory is infinite but it is actually a subset. We only choose axioms in math that are internally consistent. The number Inconsistent sets of axioms are a huge and many are discarded to find a consistent set. It is possibly this blurry demarcation of restriction and size of the domain that marks our intuitive feelings of what we label as "created" or "discovered." Who knows, I suspect the rules are much more complicated and if we dive in deeper you will find that our intuition is flawed. For example why does it feel extremely wrong to say that the Americas were created rather than discovered? But again, realize that we are discussing the intricacies of arbitrary words defined in language. Outside of the domain of language the concept is uninteresting.