Suppose acomputer memory were infinitely fast and computer memory were free would you have any reasion to study algorithm yeas or no why?

Answer 1

If there was some magical infinitely fast infinite memory computer then a brute force algorithm would have the same running time as an elegant algorithm, so in that case it wouldn't make any difference. However, there is no such thing as an infinitely fast computer or free memory, in the real world you have to make trade-offs and know how those affect your memory-usage and running-time.

Also, unless you know algorithms you are going to have a VERY hard time trying to code any sort of advanced functionality, especially things like encryption which depend on strong randomness, and where a small mistake anywhere in your algorithm can mean that your encryption can be easily compromised by someone who knows what they are doing.

Answer 2

Yes. There are problems for which an algorithm cannot exist. See "The Halting Problem" and other classes of unsolvable problems. Attempting to solve these problems algorithmically is logically impossible, even given infinite resources.

If the question is simply comparing sorting algorithms for in-memory lists -- no, there is not a reason. However, algorithms are applied to other things that you have not specified as infinite fast and plentiful, such as network bandwidth, hard disk capacity/rotational speed, etc.