A few times lately I've told myself how much of a fraction of the 60 I'd done so far. It amused me to do six pushes then think "one-tenth done!" But then I remembered that 10 out of 60 is one-sixth, then 12 out of 60 is one-fifth: not much, but it meant that with two more reps I'd gone from one-sixth to one-fifth. That's one way to note progress. I can make progress.
So 15 reps: 1/4. 20 reps: 1/3. 30 reps: 1/2 (ooo, I can use ½!) 35 reps: 35/60, or 7/12. 42 reps: 7/10. (43 reps: 43/60. That doesn't reduce, unless you switch to decimals, which'd be .71666666... and so on into infinity, which math can express better than me.) Which gets me closer to the goal each time of 60 out of 60. Or, 1. And then, in the future, more push-ups and more upper body strength.
Maybe I'm strengthening my mind as well as my body. Hmm.