# Why does Limit not compute simple limits involving integer parts?

I asked Mathematica to compute for me the following limit:

Limit[IntegerPart[M a]/M, M -> Infinity]

Whatever a is, the limit should come out as a. Indeed, this is the result whenever I plug in any explicit value of a. Unfortunately, as stated above, the limit does not compute (Mathematica returns exactly the same formula). I tried simplifying the expression with some extra assumptions on a (thinking that maybe Mathematica isn't sure that a is a real):

FullSimplify[Limit[IntegerPart[M a]/M,M->\[Infinity]], Assumptions-> a > 1]

but this does not help. Any advice on what I'm doing wrong?

• I get ConditionalExpression[a, a > 0] in MMA 11.3. – Anjan Kumar Jan 12 '19 at 15:23
• Hm... I'm in Mathematica 9.0. – Jakub Konieczny Jan 12 '19 at 15:24
• Limits in Mma have come a long way since V9.0....especially on functions that are not analytic/meromorphic. – Michael E2 Jan 12 '19 at 16:22