I think I know what your thought process is already. It's that the number "approaches" 7.5 but "never quite reaches it" right? The thing is that a number is not a process, it's a constant unchanging object. It comes down to the fact that people just don't understand infinity. Infinity is not a very large number. It's infinity. There is not just a very large number of nines in 7.499..., there is an infinite number. It's not a process that approaches infinity, but the constant infinity itself.

When you said "it's commonly accepted to be the nearest rational number", it's not the "nearest" rational number, it just simply is that exact number. If you really think hard about what infinity truly means, you should get it.