If you move along any axis less than the hardcoded value of 1e-7 (or 0.0000001) — the movement gets canceled. This brings us to the collision checks. When you're about to collide with a block — Minecraft doesn't let you do it and sets your position next to the edge of a block so the distance to it is about 1e-8. Then the game squares the movement vector and if the result is less than 1e-7 — movement gets canceled.
But if you're about to step (for example, from the slab, or to the slab, or otherwise move up half a block or less), the checks will run like that:
First check — sees your movement is greater than 1e-7 -> sees you're about to collide with the block -> sees that you need to make a step -> sets your position to 1e-8 from the block and makes a step (moves you half a block higher).
Second check — sees that your movement vector squared is greater than 1e-7 (since you're also moving upwards) and doesn't do anything.
Then the game checks the collision with the top block. If there's nothing — the game lets you move further. If there's a block, it again sets your position next to the edge, but still thinks that you're standing on the block that gives you a little time gap to make a jump.

Here you can find more detailed explanation of how this mechanics works (*click*).