Timeline for How could the people of the past be sure that $a \times b = b \times a$?
Current License: CC BY-SA 4.0
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| May 4 at 22:17 | history | edited | Michael Hardy | CC BY-SA 4.0 |
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| Aug 7, 2023 at 3:45 | comment | added | Michael Hardy | However, as soon as someone did have the concept of multiplication as described in my answer above, I think this argument would be seen quickly. | |
| Aug 7, 2023 at 3:44 | comment | added | Michael Hardy | @MichaelBächtold : Recall Euclid's proof of the infinitude of primes: if $S$ is any finite set of primes then the prime factors of $1+\prod S$ are not members of $S,$ so there are always more primes. But Euclid did not write about multiplying the members of $S,$ but rather about finding their smallest common multiple. For distinct primes, the result is the same as that of multiplying them. But if someone lacks the concept of multiplication, then simple propositions about multiplication would not be obvious to that person. However$,\,\ldots\qquad$ | |
| Aug 6, 2023 at 5:16 | comment | added | Michael Bächtold | What is obvious to us must not necessarily agree with what was obvious to people in the past. I believe there are quite a few examples of this. | |
| Aug 4, 2023 at 17:17 | comment | added | Michael Hardy | @MichaelBächtold : I was giving an obvious explanation. I was pointing out that this could not have failed to be obvious to anyone who had the concept of multiplication. | |
| Aug 4, 2023 at 9:10 | comment | added | Michael Bächtold | Being a site on history of science and math, I'd expect some references to historical works. You are just giving a plausible explanation. | |
| Aug 3, 2023 at 0:57 | history | edited | Michael Hardy | CC BY-SA 4.0 |
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| Aug 2, 2023 at 18:55 | history | answered | Michael Hardy | CC BY-SA 4.0 |