New answers tagged surreal-numbers
10
votes
Do the surreal numbers enjoy the transfer principle in ZFC?
A partial answer to the focused question: it's not provable in ZFC that there is an OD class $\mathbb{Z}^*$ such that $(\mathbb{R}, +, \cdot, \mathbb{Z}) \equiv (\mathrm{No}, +, \cdot, \mathbb{Z}^*).$ ...
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16
votes
Do the surreal numbers enjoy the transfer principle in ZFC?
In $\mathsf{ZFC}$ if any two proper class models of the theory of an infinite set are isomorphic, then global choice holds. This is because $V$ and $\mathrm{Ord}$ are both models of this theory and an ...
- 12.4k
9
votes
Are periodic functions such as sine and cosine defined on surreal numbers?
Since the surreal numbers form a saturated real-closed field, it follows that they serve as a (proper class) version of the hyperreal numbers, including the transfer principle. This means that ...
- 236k
0
votes
In hyperreal field, can ln(ε) and ln(ω) be expressed as infinite sums?
I will propose an answer my question. Please let me know if I have spoken accurately.
Within the hyperreal field (that is, the most traditional hyperreal field as described by some of the original ...
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8
votes
In hyperreal field, can ln(ε) and ln(ω) be expressed as infinite sums?
To help avoid any misunderstanding that may arise for readers of this question, let me say that when understood in the usual sense, there are no nontrivial convergent sequences or series at all in the ...
- 236k
3
votes
In hyperreal field, can ln(ε) and ln(ω) be expressed as infinite sums?
For positive $\epsilon$, the expression $\ln \epsilon$ will be equal to its power series at $x=1$ (in the $\delta, N$ sense).
To help avoid any misunderstanding that may arise for readers of this ...
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