It's functionally infinite, because it's bounded by encoding time, not storage capacity. If you spent your entire life learning you would not learn enough to exhaust your long-term memory.
This is a very basic fact about human memory that you can find in any psych 101 textbook. You should consider picking one up and reading it.
The underlying assumption being that you won't live much longer than anyone else. Hopefully this will change, and soon. Do those psych textbooks make any guesses to how long an average human would have to live before they exhausted their brain's storage capacity?
I am reminded of the immortal character in Douglas Adam's Dirk Gently's, who has been alive too long and forgotten all of his early life (including who he is). I believe he was supposed to be a Time Lord.
This is close to the truth – that character was not supposed to be a Time Lord in the book, but the storyline of the book is loosely based on two separate scripts written by the same author for two separate Doctor Who serials. (For unrelated reasons, the one script containing that character was only partially filmed, and the serial was therefore not broadcast at the time.)
This is a very basic fact about human memory that you can find in any psych 101 textbook. You should consider picking one up and reading it.