[hcs]

An algorithm is a finite sequence of instructions, and so can't include an infinite table. More generally, https://en.wikipedia.org/wiki/Effective_method

[charcircuit]

I disagree. 1 step is a finite sequence of instructions.

[SkiFire13]

The lookup table is part of the algorithm, and is not finite.

In general any problem can be solved in 1 step with a lookup table, so here you go P=NP solved.

[charcircuit]

It doesn't have to be part of the algorithm. It all depends on how you measure it.

[hcs]

Well, yes, which is why they don't measure it your way, as it doesn't lead to discovering anything interesting about computation to have a shortcut like that. Or if they do it's part of a larger analysis, called an oracle machine.

[charcircuit]

I am against statements like:

A: "X people don't know how to do Y"

B: "Why not do Z?"

A: "Z is too easy and boring so they actually added more restrictions to how you are allowed to do Y so that solution doesn't count"

[hcs]

Maybe I'm not communicating the point clearly. In order to use a table to do the whole multiplication it has to be much larger than the largest number you would want to multiply with it. A lot of the analysis of algorithms, especially multiplication as discussed here, is about astronomically large numbers, so you don't want the existence of an even more astronomically large table as a prerequisite.

[SkiFire13]

Yup, and everyone measures it to be part of the algorithm, otherwise you start getting nonsensical results.