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Counting is matching

A number is a name for how many things you matched.

Why this exists

Before anyone wrote a number, a shepherd still needed to know if the flock had come home. They matched one pebble to one sheep. If a pebble was left with no sheep, an animal was missing.

The pebbles were not the sheep. They were a record of the sheep. A number is that kind of record, given a short name.