By induction there will be limits no matter what. You cannot have an infinite amount of memory in your head. You cannot have an infinite amount of anything anywhere.
However abstract something is, the symbolic nature of an abstraction must utilize at least one atom. For example, let's say we have a big number... <the number nine> that we want to abstract. We can choose to have that number be represented by a single symbol "9" rather than nine actual things. This is the true nature of what abstraction is, using smaller symbols to represent bigger things aka compression. But for that symbol to even exist it must be written down or memorized somewhere. This takes up physical space. Even your computer hard drive must use physical magnets flipped to different polarities to represent memory.
The biggest possible abstraction of a real world phenomena in terms of magnitude is to represent the entire universe with a single atom. In the end atoms take up space and even the biggest possible abstraction of the entire universe must take up the space of at least one atom. Your memories are no different... they are just symbols representing aspects of your life experience. Likely your memories take up much more space than a single atom and if your memories take up space and you have a finite amount of space in your skull, then by logic your memory is finite... this categorically true by logic.
Whether the finite memory problem is solved by garbage collection or whether it's not solved at all and people simply go insane is undetermined.
What is known for sure is that your memory is finite.
Using symbols to represent bigger concepts is a form of compression. The representation/memory of an animal in your mind is done using symbols rather than an actual animal.
This isn't speculation. A animal exists in reality as construction of millions of biological cells each in turn made up of billions of atoms. Depending on how big the animal is it could be more atoms that make up your brain. Therefore, for the animal to exist in your mind as a memory there Must be a form of information compression. You cannot fully hold an actualization of an animal in your mind because it is too big to exist in your mind. Your brain holds symbols of the animal.
What happens with a jpeg is the exact same concept as what happens in your memory. A jpeg is a symbolic representation of the actual picture. It is a form of lossy compression because details from the original picture are lost.
There is no difference between losing information during lossy compression and deleting information during lossy compression. Lossy compression means that data is literally lost aka deleted.
You can compress an entire memory into a single bit or into nothing. Lossy compression is a gradient where maximum space saving involves total deletion. Medium space spacing involves partial deletion and no space saving aka lossless compression involves no deletion.
Let me put it this way. A JPEG is lossy compression, there is literally deleted information when you compress a picture into a JPEG that cannot be retrieved. Do you understand this concept about the pictures you see on the internet? If you decrease the size when saving a jpeg in photoshop you actually lower the image quality to the point where you can lose a ton of information (aka deletion).
A png is an example of compression without loss. Same with zip, tar or rar file. The original file can completely be rebuilt from a a non lossy compressed file BUT NOT a JPG because a jpeg is a lossy compression. Get it?
Please thank me for teaching you. Or don't reply because you're too mad at being wrong and not appreciative of the fact that I didn't "give up" on a you.