1) To a computer the number line is not solid like they draw it in mathematics. Instead it looks like the dots and dashes of morse code. This is because some numbers do not exist for a computer. For instance there is no 1 / 3 on its number line, just a big hole.
2) (a - b)(a+b)≠(a^2 - b^2). Algebraically equal expressions are not equal to a computer.
3) Addition is not commutative.
The order of addition can drastically affect the answer!
4) A computer can not subtract or multiply without possible disastrous error.
5) You never use the quadratic formula to solve a quadratic equation because on a computer it might give inaccurate results.
6) Newton's iteration though taught is rarely the best one for the job.
7) A computer can not always compare theoretically equal quantities.
8) There is a largest number to a computer.
9) A computer can have three states for a matrix, singular, non singular and nearly singular!
Like everything else, machines do it better.
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
I may have been a bit hasty when I wrote that. I meant to say a lot better.