Here, to clarify what "do with real numbers" mean: 1. All inputs are integers; 2. Numbers may get calculated to get irrational results. 3. Outputing floor(result) is enough.
Now, for what operators in 2, the above is possible?
E.g. Allowing sqrt, and when we are calculating floor(1+sqrt(2)-sqrt(2)), if we directly compare every digits to judge whether 1+sqrt(2)-sqrt(2)<1, it falls into an infinite loop. Some models allow both 1.000 and 0.999 as (1+sqrt(2)-sqrt(2)), but here it's not allowed.