It’s annoying to remember the grammar rule for quantities that dictates when to use many vs. much, fewer vs. less, etc.

Shockingly enough, knowing the concept of countability in math makes it easy. Or as easy as English can be, anyway.

## Countable

Bijection with (not necessarily proper) subset of natural numbers, $$\mathbb{N}$$.

## Uncountable

Not in bijection with a subset of the natural numbers.

## Heuristic for telling which one without rigorous proof

Think discrete vs. continuous quantities.

## Examples

countable uncountable
many much
fewer less