Mathematical concepts don't have to have an obviously physical analogue. I mean, you'd find it difficult to observe minus two apples and certainly tricky to observe i apples.
To my mind, maths is like a "what if?" puzzle and whether or not infinity makes sense in the physical world, there's still fun to be had by considering the consequences of it.
That also means that it can be interesting to consider limited number systems which don't have any concept of infinity.
No. I believe that is more apples than there are atoms in the universe, so not only it is impossible to observe, it is a fundamental contradiction with our universal reality. No one and nothing will ever be able to observe or interact that many apples, and so a reference to that many apples is only an abstract mathematical convenience that has no direct bearing to reality.
Like infinity.
I'm not sure I actually believe that, I'm just thinking out loud. But it leads me to think the question "Does infinity exist?" should be answered with the question "An infinity of what?"
Some might say that 2 is as made up as infinity.
Let me elaborate a little - your brain together with society made an abstraction "apple", and only by not distinguishing between these "sets" of atoms you can have numbers.
Well do you say it or are you just playing devils advocate? The post you are responding to seems very straightforward.
If you wanna go all philosophical, “real” might just be anything that is useful. In that way infinity is real because you can use it to do calculus. On the other hand, there are ways of doing calculus that do not involve thinking about infinity. But if you’re gonna count to three apples you pretty much have to go through “two” no matter what.
To my mind, maths is like a "what if?" puzzle and whether or not infinity makes sense in the physical world, there's still fun to be had by considering the consequences of it.
That also means that it can be interesting to consider limited number systems which don't have any concept of infinity.