L'Hôpital's Rule is Equivalent to the Least Upper Bound Property
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912401161453568 |
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| author | Grant, Martin Hambrook, Kyle Rusterholtz, Alex |
| author_facet | Grant, Martin Hambrook, Kyle Rusterholtz, Alex |
| contents | We prove that, in an arbitrary ordered field, L'Hôpital's Rule is true if and only if the Least Upper Bound Property is true. We do the same for Taylor's Theorem with Peano Remainder, and for one other property sometimes given as a corollary of L'Hôpital's Rule. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_23092 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | L'Hôpital's Rule is Equivalent to the Least Upper Bound Property Grant, Martin Hambrook, Kyle Rusterholtz, Alex Classical Analysis and ODEs 12J15, 12J25, 26A03, 26E30, 97I99 We prove that, in an arbitrary ordered field, L'Hôpital's Rule is true if and only if the Least Upper Bound Property is true. We do the same for Taylor's Theorem with Peano Remainder, and for one other property sometimes given as a corollary of L'Hôpital's Rule. |
| title | L'Hôpital's Rule is Equivalent to the Least Upper Bound Property |
| topic | Classical Analysis and ODEs 12J15, 12J25, 26A03, 26E30, 97I99 |
| url | https://arxiv.org/abs/2505.23092 |