>infinity itself is something that cannot be embedded in a finite program
I am not sure what you mean by infinity here, but there are many ways in programming to handle infinite streams in an otherwise finite program. Python's itrrtools.count and the ability to map and filter over it would be a basic example.
Indeed I could argue that every game's or webserver's event loop is embedding infinity in a finite program.
The symbol is not an actual infinity. The abstract concept we access with our minds is an actual infinity. That's the point. The abstract principle cannot itself be embedded in a program or symbol. All we can do is describe it with rules we infer from observing it. Like a painting of a tree will never be the tree itself, and we will not be able to infer everything about the tree just by looking at the painting.
I am not sure what you mean by infinity here, but there are many ways in programming to handle infinite streams in an otherwise finite program. Python's itrrtools.count and the ability to map and filter over it would be a basic example.
Indeed I could argue that every game's or webserver's event loop is embedding infinity in a finite program.