All Questions
Tagged with real-numbers abstract-algebra
20
questions
3
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136
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Is there an ordered field with distinct subfields isomorphic to the reals?
Is there an ordered field with distinct subfields isomorphic to the field $\mathbb R$ of real numbers?
- 19.9k
2
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2
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Is there a reasonable limit to how far you can generalise complex numbers? [duplicate]
Real numbers satisfy a(bc) = (ab)c as well as ab = ba. They are also comparable.
Generalising to complex numbers, everything stays the same, except the numbers lose their comparibility.
Generalising ...
- 195
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answer
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Is every ring homomorphism between real algebras also real-linear?
$\def\bbR{\mathbb{R}}
\def\bbQ{\mathbb{Q}}$The comment from Vladimir Sotirov in March 2022 in this answer could be interpreted as suggesting the possibility that every ring homomorphism between $\bbR$-...
1
vote
1
answer
85
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Are these two mathematical objects the same from a practical standpoint, or literally identical mathematical objects? [closed]
This question is derived from another question that I recently asked.
Take the two mathematical objects $\{ \mathbf{x} \in \mathbb{R}^n \mid x_1, x_2, \ldots, x_n \in \mathbb{Z} \}$ and $\{ \mathbf{x}...
- 4,322
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Proof on Rational Numbers
I am trying to determine whether the following structure forms a Ring under the Real Number Definition of Addition and Multiplication
Consider the set of Real Numbers of the form:
$A = \{a + bp \:|\:...
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