When people say one thing is infinitely better, worse, easier, or more interesting than another, they mean the gap is huge — so big that putting the two side by side almost feels unfair. You hear this most in comparisons: infinitely more patient, infinitely preferable, infinitely more complicated. It is not slang, but it is not a maths class either; careful speakers and writers like it. Though actually, they almost never mean “with no end at all.” They are borrowing the old idea of “no limit” to say “very, very much more.” In maths and philosophy, infinitely can still keep the stricter sense: going on without stopping. In ordinary talk, the comparison use is the one you will meet first.