>They won't have a concept of zero? They won't have a concept of 1=successor(0)? I find this very, very hard to believe

Most of the world did mathematics for a long time without zero (I hope you know that most number systems like Roman didn't have zero till that eventually came from India, and we evolved to have the current number system). Who knows what direction different number systems might have taken if they didn't come in contact with zero.

That's mostly irrelevant. The naturals starting from 1 are isomorphic to the naturals starting at 0, which is why math didn't need zero for so long.

How is it irrelevant to this discussion? Parent proposed that aliens will have zero by posing that question. I gave an example from our own earth indicating intelligent life can manage without zero.

> I gave an example from our own earth indicating intelligent life can manage without zero.

Firstly, I disagree that humanity managed without zero. Literally everyone had an intuitive understanding of zero, they just didn't have it in their formal systems that were being studied by philosophers. For instance, try walking walking up to a vendor in Ancient Greece and just taking something without paying.

Secondly, it's largely irrelevant because a lot of math with zero can be mapped to math without zero with no loss of information, so even if aliens used math without zero there would be no trouble communicating as there would still be an understandable formal correspondence.

Not if you take into account the special properties of 0. (Generally speaking, a structure that admits a neutral element with respect to addition is not isomorphic to one that does not.)

You are correct, hence why I initially said it's mostly irrelevant. I should have qualified the claim about isomorphism as well. Still, quite a bit of math maps 1:1 without zero, so you can build a common understanding even if they don't have zero.

I also don't think any alien species with which we will communicate will not understand zero. It just seems impossible. Before philosophers came up with zero in formal models, everyone intuitively understood the concept. Every animals knows when they have no food vs. when they have some food. Humans in ancient civilizations also couldn't just take something without paying.