ShiroKuro Like, I don’t care about that 2 or 1, if I’m at the keyboard, I know where to put my hands, isn’t that enough!
I had a conversation about names a while back. If you do music (or anything) on your own, you don't need names. If there are two or more of you, maybe you can refer to a musical thing by humming or tapping it, or pointing - otherwise you need names. I translated the internship of a dental assistant. Her first step was to memorize the names of all the instruments she'd be handing the dentist. If the dentist could just grab his own tools from a drawer, those tools could stay nameless. Names are for communication.
What you're dealing with is the span of an octave which goes from one C up to the next C, so from C to B. You can think of the numbers as a "house". C4 starts the "4 house". C, and everything above it belongs to the 4 house - so the next A above that C is A4.
Names are artificial and theory is often taught abstractly. "Own" these names at the piano, using your senses. I'd start with C4, because middle C (which is C4) is our reference point. We sit at middle C. Span your hand from C4 to the B above it and see that whole span of notes - your house of 4. Tell yourself this is 4. Poke some notes within that span with your other hand, telling yourself "A4, F#4, B4". Do that with other octave ranges. Do this briefly a couple of times in a day. When you're playing music, stop suddenly, look at where your hand is, and "Ah, I'm in 3 right now with my LH." This works better than cramming.
Names are also artificial, whereas reality is "more". The word "cork" has us picture a material made of spongy wood: "bouchon" and "Stopfen" has us picture the act of closing up a hole. The actual thing is more than either, and often a cork isn't even made of cork. A4 is artificial. Why C to C? why not A to A? Or "F to F"? The name "middle C" at least is real for pianists, because it's where we sit - at the middle. It's also in the middle of the grand staff. But C4? But the names are what they are because people invented them, and the 1, 2, 3, 4 seems to be the common convention now.
