What is the meaning of $ mathbbR bmod T$?

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What is the meaning of $ mathbbRbmod T$ for a fixed $T>0$. The set of all equivalence classes?

And how can I derive a function of the form $f:mathbbR^d to mathbbRbmod T$?

derivatives differential-geometry algebraic-topology modules

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edited Jul 16 at 9:40

Bernard

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asked Jul 16 at 8:15

Thomas_R

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up vote
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down vote

favorite

What is the meaning of $ mathbbRbmod T$ for a fixed $T>0$. The set of all equivalence classes?

And how can I derive a function of the form $f:mathbbR^d to mathbbRbmod T$?

derivatives differential-geometry algebraic-topology modules

share|cite|improve this question

edited Jul 16 at 9:40

Bernard

110k635103

asked Jul 16 at 8:15

Thomas_R

296

add a comment | 

up vote
2
down vote

favorite

up vote
2
down vote

favorite

What is the meaning of $ mathbbRbmod T$ for a fixed $T>0$. The set of all equivalence classes?

And how can I derive a function of the form $f:mathbbR^d to mathbbRbmod T$?

derivatives differential-geometry algebraic-topology modules

share|cite|improve this question

edited Jul 16 at 9:40

Bernard

110k635103

asked Jul 16 at 8:15

Thomas_R

296

What is the meaning of $ mathbbRbmod T$ for a fixed $T>0$. The set of all equivalence classes?

And how can I derive a function of the form $f:mathbbR^d to mathbbRbmod T$?

derivatives differential-geometry algebraic-topology modules

share|cite|improve this question

edited Jul 16 at 9:40

Bernard

110k635103

asked Jul 16 at 8:15

Thomas_R

296

share|cite|improve this question

share|cite|improve this question

edited Jul 16 at 9:40

Bernard

110k635103

edited Jul 16 at 9:40

Bernard

110k635103

edited Jul 16 at 9:40

Bernard

110k635103

110k635103

asked Jul 16 at 8:15

Thomas_R

296

asked Jul 16 at 8:15

Thomas_R

296

asked Jul 16 at 8:15

Thomas_R

296

296

add a comment | 

add a comment | 

1 Answer
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I would assume

$$
x equiv y mod T Leftrightarrow exists n in mathbb Z: x- y = nT.
$$

This then yields a quotient group (namely, the one of $(mathbb R, +)$ divided by the subgroup $n in mathbb Z$) with well-defined addition.

Your function would then come from the composition $mathbb R^d to mathbb R$ (eg. the projection) with the quotient map $mathbb R to mathbb R / langle T rangle$.

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answered Jul 16 at 8:21

AlgebraicsAnonymous

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1 Answer
1

active

oldest

votes

1 Answer
1

active

oldest

votes

active

oldest

votes

active

oldest

votes

up vote
2
down vote

I would assume

$$
x equiv y mod T Leftrightarrow exists n in mathbb Z: x- y = nT.
$$

This then yields a quotient group (namely, the one of $(mathbb R, +)$ divided by the subgroup $n in mathbb Z$) with well-defined addition.

Your function would then come from the composition $mathbb R^d to mathbb R$ (eg. the projection) with the quotient map $mathbb R to mathbb R / langle T rangle$.

share|cite|improve this answer

answered Jul 16 at 8:21

AlgebraicsAnonymous

69111

add a comment | 

up vote
2
down vote

I would assume

$$
x equiv y mod T Leftrightarrow exists n in mathbb Z: x- y = nT.
$$

This then yields a quotient group (namely, the one of $(mathbb R, +)$ divided by the subgroup $n in mathbb Z$) with well-defined addition.

Your function would then come from the composition $mathbb R^d to mathbb R$ (eg. the projection) with the quotient map $mathbb R to mathbb R / langle T rangle$.

share|cite|improve this answer

answered Jul 16 at 8:21

AlgebraicsAnonymous

69111

add a comment | 

up vote
2
down vote

up vote
2
down vote

I would assume

$$
x equiv y mod T Leftrightarrow exists n in mathbb Z: x- y = nT.
$$

This then yields a quotient group (namely, the one of $(mathbb R, +)$ divided by the subgroup $n in mathbb Z$) with well-defined addition.

Your function would then come from the composition $mathbb R^d to mathbb R$ (eg. the projection) with the quotient map $mathbb R to mathbb R / langle T rangle$.

share|cite|improve this answer

answered Jul 16 at 8:21

AlgebraicsAnonymous

69111

I would assume

$$
x equiv y mod T Leftrightarrow exists n in mathbb Z: x- y = nT.
$$

This then yields a quotient group (namely, the one of $(mathbb R, +)$ divided by the subgroup $n in mathbb Z$) with well-defined addition.

Your function would then come from the composition $mathbb R^d to mathbb R$ (eg. the projection) with the quotient map $mathbb R to mathbb R / langle T rangle$.

share|cite|improve this answer

answered Jul 16 at 8:21

AlgebraicsAnonymous

69111

share|cite|improve this answer

share|cite|improve this answer

answered Jul 16 at 8:21

AlgebraicsAnonymous

69111

answered Jul 16 at 8:21

AlgebraicsAnonymous

69111

answered Jul 16 at 8:21

AlgebraicsAnonymous

69111

69111

add a comment | 

add a comment | 

 

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