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Good Math by Mark C. Chu-Carroll

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5Zero

When we look at strange numbers, the starting place has to be zero. Zero may not seem strange to you because you’re used to it. But the idea of zero really is strange. Think about what we said numbers mean: if you think in terms of cardinals and ordinals, in terms of counting and position, what does zero mean?

As an ordinal, what does it mean to be the zeroth object in a collection? And what about zero as a cardinal? I can have one something and count it. I can have 10 somethings and count them. But what does it mean to have zero of something? It means that I don’t have any of it. So how can I count it?

And yet, without the concept of zero and the numeral 0, most of what we call math would just fall apart.

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