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15
165
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Interpretation of the transfer principle.

Published on
#logic #nonstandard-analysis #nonstandard-models
298
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Cauchy sequence for $0$ in non-standard analysis

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#real-analysis #sequences-and-series #cauchy-sequences #nonstandard-analysis #infinitesimals
64
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Problem from Keisler infinitesmal calculus book.

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#nonstandard-analysis
79
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Nonstandard analysis without transfer principle and mathematical logic

Published on
#nonstandard-analysis
147
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Is it possible to replace hyperreal numbers with "good enough" alternatives?

Published on
#soft-question #nonstandard-analysis #ordered-fields
65
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If $a_i/b_i$ converges then $\Sigma_m^na_i$ is infinitesimal iff $\Sigma_m^nb_i$ is too

Published on
#sequences-and-series #nonstandard-analysis
58
Views

Finite field with infinitesimals / nonstandard analysis over finite fields

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#finite-fields #nonstandard-analysis #nonstandard-models
203
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Thoughts about allowing arithmetic with infinitesimals to (mostly) solve limits, can it be done without contradictions?

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#real-analysis #limits #number-systems #nonstandard-analysis #infinitesimals
159
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Expressing trigonometric functions of infinitesimal arguments as algebraic quantities/elementary functions

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#real-analysis #trigonometry #taylor-expansion #nonstandard-analysis #infinitesimals
104
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Why isn't $\mathcal{P}(^*A)\subseteq {^*}\mathcal{P}(A)$?

Published on
#logic #set-theory #nonstandard-analysis #nonstandard-models
120
Views

How big do hyper-reals get?

Published on
#nonstandard-analysis #big-numbers
144
Views

Is it possible to extend the domain and range of a function that maps from R to R to other sets?

Published on
#abstract-algebra #nonstandard-analysis #infinitesimals
180
Views

What is the motivation for building the hyperreals using an ultrapower construction?

Published on
#real-analysis #abstract-algebra #field-theory #nonstandard-analysis
586
Views

Ultraproduct of a metric space

Published on
#logic #metric-spaces #model-theory #nonstandard-analysis #metric-geometry
279
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Fourier transform and non-standard calculus

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#fourier-analysis #hilbert-spaces #fourier-series #distribution-theory #nonstandard-analysis

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