[yters]

Let's say I have a computer that can only store 10 bits worth of information, but generates 100 bits of information. Then obviously the information cannot entirely originate in the computer.

[ukj]

Sure it can. Compression. Kolmogorov complexity.

I don't need to 'store' the infinite set of natural numbers - that would require infinite space (memory).

But I can describe the infinite set in a single line of Python. Nat = lambda x=0: Nat(x+1)

It's just a space-time tradeoff.

[yters]

If the sequence isn't compressible, then you can eliminate that possibility.

[ukj]

You can never determine this with 100% certainty - that is what we have falsification for.

The non-compressibility of a sequence is a falsifiable claim.

All it takes is a single demonstration of successful compression.

[yters]

for limited runtime you can

[ukj]

So you were unable to compress the stream given the allocated time.

Perhaps you could've compressed it had you kept running for just a second longer?

[yters]

i mean run all the shorter bitstrings until time runs out or they terminate.