Questions tagged [arithmetic]

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Is multiplication postulated axiomatically in Peano arithmetic?

I figured this question is better suited to this stackexchange. I give some mathematical details, but this is primarily an HSM question. According to this post, the existence of multiplication in ...
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2answers
259 views

Why did the romans use IV and why doesn't it overcomplicate things?

Ok so if the Romans did not use things like IX and IV and XC etcetera then addition and subtraction would be almost as instant as it is in our number system. However with the new system it seems to me ...
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Was the idea that the result of division of positive number by negative number should be negative ever been controversial?

If we divide a positive number by another positive number, the result becomes greater as the divisor becomes smaller. If we continue this logic, division by a negative number should be greater than ...
4
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0answers
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Where is First-Order Peano Arithmetic first clearly formulated?

I really should know this, but ... When/where/by whom was first-order Peano Arithmetic first clearly and explicitly formulated in a recognizably modern form (perhaps exact notation apart) -- with the ...
6
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2answers
384 views

Did Archimedes view fractions as "numbers"?

For quite some time I had the wrong impression that classical Greek mathematicians didn't use fractions. (I don't remember where I had this from.) But I recently looked into Heath's book about ...