Timeline for answer to A curiosity: how do we prove $\mathbb{R}$ is closed under addition and multiplication? by Jack D'Aurizio
Current License: CC BY-SA 4.0
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| Dec 12, 2018 at 4:10 | history | edited | Jack D'Aurizio | CC BY-SA 4.0 |
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| Dec 12, 2018 at 4:09 | comment | added | Jack D'Aurizio | @XanderHenderson: fair point, I should have written it. When defining Cauchy/convergent sequences, the $\varepsilon$s live in the original ordered, Archimedean set. | |
| Dec 12, 2018 at 4:08 | comment | added | Xander Henderson♦ | Where do your $\varepsilon$s live? If you are not careful, your construction runs the risk of being circular. Typically, when we talk about metric spaces, the target space of the metric is the real numbers, which you haven't defined yet. | |
| Dec 12, 2018 at 4:07 | history | edited | Jack D'Aurizio | CC BY-SA 4.0 |
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| Dec 12, 2018 at 4:00 | vote | accept | PrincessEev | ||
| Dec 12, 2018 at 4:54 | |||||
| Dec 12, 2018 at 3:59 | history | edited | Jack D'Aurizio | CC BY-SA 4.0 |
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| Dec 12, 2018 at 3:52 | history | answered | Jack D'Aurizio | CC BY-SA 4.0 |