on the other hand, technically nothing is turing complete because of lack of infinite memory
> Real computers constructed so far can be functionally analyzed like a single-tape Turing machine (the "tape" corresponding to their memory); thus the associated mathematics can apply by abstracting their operation far enough. However, real computers have limited physical resources, so they are only linear bounded automaton complete. In contrast, a universal computer is defined as a device with a Turing-complete instruction set, infinite memory, and infinite available time.
https://en.m.wikipedia.org/wiki/Turing_completeness#Non-math...
Not going to keep replying as this is not really a point I am going to get convinced of - to be technically turing complete is to show that every thing computable by a turing machine is computable by your construct. This is not possible in a memory constrained system.
a turing machine is something way more specific than just "something that can execute algorithms" though, it's a machine that executes them using a specific system and constraints (namely advancing and modifying a strip of tape). So calling anything that can compute what a turing machine can compute a turing machine would be inaccurate just by merit of that.
of course ultimately you're right though, words mean what they're used to mean, so turing completeness excludes the infinite memory constraint, my initial comment wasn't really meant fully seriously, just being a smartass for a joke.
When we say something is Turing complete, there’s always an implicit “if it ran on a computer with unlimited memory” assumption that comes with it, because no computer with limited memory can ever simulate all Turing machines. You can always construct a Touring machine that makes a given computer run out of memory.
So technically, no real computer or computer program is Turing complete, or able to accurately simulate any Turing machine. The whole thing is an irrelevant technicality though, as A) we have so much memory available that we might as well treat it as unlimited and B) touring completeness is a theoretical property - if you prove it for something like python type hints, that proof won’t assume any memory limitations, ie. it’ll assume the computer the thing runs on has infinite memory. The proof is valid even though no such infinite computer actually exists.
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It's a ... uh ... a recursive parallel processing algorithm. Yeah.