ChatGPT so bad at Math; Inconsistency in answers; Some insight on how it works from its own words.

ChatGPT is so bad at Math; Inconsistency in answers; Some insight on how it works from its own words. ChatGPT answers these questions:

(1) if a+1 = 0, then a+2 = 1.
answer (Wrong): This statement is false. If a + 1 = 0, then a = -1. Therefore, a + 2 = -1 + 2 = 1.
(2) if b-1=c-2, then c-b=1
(3) the set of positive integers and the set of prime numbers, which set is bigger?
(4) how many prime numbers are there?
(5) there are an infinite number of rooms in a hotel, and all the rooms are occupied, construct a way to have one more person move into the hotel. is it possible?
(6) if I teach you something, will you remember it, and next time someone else asks about it, you can give the person this answer?
(7) give an answer to the same question, but you can only use 2 milliseconds to search for the answer.
(8) is the answer in your memory or in a database, or somewhere else?
(9) where do the patterns reside?
(10) how do you share memories with other copies of you that are serving other people?
(11) if not sharing how do you ensure that what you've learned can propagate to other instances?
(12) are our conversations part of the knowledge for the next version?