Can a pokemon be level 21.5 when caught in wild if your trainer level is 21?

You can only catch odd level integer Pokemon. 1,3,5,7....etc

I've heard that all integer levels are captureable. What could have caused the confusion if this is so is people describing the "half-levels" as "levels", and so noting that every only every other "odd level" of pokemon can be caught in the wild, with the people who refer to "odd levels" as every "fourth" (Odd.5, Even, Even.5, Odd) level interpreting this differently.