[fjsolwmv]

You can do discrete math (including analysis of algorithms) without reals.

Reals are only needed for calculus on infintesimals, which are not relevant to much of CS. Everything you can do with formal Taylor expansions doesn't need reals. In fact knowing calculus on the reals often causes confusion in students learning formal expansions for CS.

[Ar-Curunir]

All of optimization, stats and theoretical ML involves solid grasp of calculus over the reals