$x = 3$ in $Bbb Z_5$ equivalent to saying $x equiv 3 pmod 5$?
I basically want to confirm the title, if I wrote both of these in a test it'd be considered the same, right?
linear-algebra
edited Dec 10 '18 at 5:47
Moo
5,53131020
asked Dec 10 '18 at 1:01
ming
3165
add a comment |
I basically want to confirm the title, if I wrote both of these in a test it'd be considered the same, right?
linear-algebra
edited Dec 10 '18 at 5:47
Moo
5,53131020
asked Dec 10 '18 at 1:01
ming
3165
1
Yes. ${}{}{}{}$
– YiFan
Dec 10 '18 at 1:25
@WillFisher The correct notation is the OP's $ xequiv 3pmod 5. $ Your notation $ xequiv 3mod 5,$ is not correct and often causes beginners to confuse relational vs. operational mod.
– Bill Dubuque
Dec 10 '18 at 3:11
add a comment |
I basically want to confirm the title, if I wrote both of these in a test it'd be considered the same, right?
linear-algebra
edited Dec 10 '18 at 5:47
Moo
5,53131020
asked Dec 10 '18 at 1:01
ming
3165
I basically want to confirm the title, if I wrote both of these in a test it'd be considered the same, right?
linear-algebra
linear-algebra
edited Dec 10 '18 at 5:47
Moo
5,53131020
asked Dec 10 '18 at 1:01
ming
3165
edited Dec 10 '18 at 5:47
Moo
5,53131020
asked Dec 10 '18 at 1:01
ming
3165
edited Dec 10 '18 at 5:47
Moo
5,53131020
edited Dec 10 '18 at 5:47
Moo
5,53131020
edited Dec 10 '18 at 5:47
Moo
5,53131020
5,53131020
asked Dec 10 '18 at 1:01
ming
3165
asked Dec 10 '18 at 1:01
ming
3165
asked Dec 10 '18 at 1:01
ming
3165
3165
1
Yes. ${}{}{}{}$
– YiFan
Dec 10 '18 at 1:25
@WillFisher The correct notation is the OP's $ xequiv 3pmod 5. $ Your notation $ xequiv 3mod 5,$ is not correct and often causes beginners to confuse relational vs. operational mod.
– Bill Dubuque
Dec 10 '18 at 3:11
add a comment |
1
Yes. ${}{}{}{}$
– YiFan
Dec 10 '18 at 1:25
@WillFisher The correct notation is the OP's $ xequiv 3pmod 5. $ Your notation $ xequiv 3mod 5,$ is not correct and often causes beginners to confuse relational vs. operational mod.
– Bill Dubuque
Dec 10 '18 at 3:11
1
1
Yes. ${}{}{}{}$
– YiFan
Dec 10 '18 at 1:25
Yes. ${}{}{}{}$
– YiFan
Dec 10 '18 at 1:25
@WillFisher The correct notation is the OP's $ xequiv 3pmod 5. $ Your notation $ xequiv 3mod 5,$ is not correct and often causes beginners to confuse relational vs. operational mod.
– Bill Dubuque
Dec 10 '18 at 3:11
@WillFisher The correct notation is the OP's $ xequiv 3pmod 5. $ Your notation $ xequiv 3mod 5,$ is not correct and often causes beginners to confuse relational vs. operational mod.
– Bill Dubuque
Dec 10 '18 at 3:11
add a comment |
1 Answer
1
active
oldest
votes
If one accepts that
$Bbb Z / (5) equiv Bbb Z_5, tag 1$
then it is evident that
$x = 3 in Bbb Z_5 = Bbb Z / (5) tag 2$
means that
$x in 3 + (5), tag 3$
that is,
$x - 3 = 5n, ; n in Bbb Z, tag 4$
i.e.,
$x equiv 3 pmod 5. tag 5$
If I were grading the test I would accept either notation as correct.
edited Dec 10 '18 at 3:12
Bill Dubuque
208k29190628
answered Dec 10 '18 at 1:22
Robert Lewis
43.7k22963
add a comment |
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1 Answer
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1 Answer
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active
oldest
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active
oldest
votes
If one accepts that
$Bbb Z / (5) equiv Bbb Z_5, tag 1$
then it is evident that
$x = 3 in Bbb Z_5 = Bbb Z / (5) tag 2$
means that
$x in 3 + (5), tag 3$
that is,
$x - 3 = 5n, ; n in Bbb Z, tag 4$
i.e.,
$x equiv 3 pmod 5. tag 5$
If I were grading the test I would accept either notation as correct.
edited Dec 10 '18 at 3:12
Bill Dubuque
208k29190628
answered Dec 10 '18 at 1:22
Robert Lewis
43.7k22963
add a comment |
If one accepts that
$Bbb Z / (5) equiv Bbb Z_5, tag 1$
then it is evident that
$x = 3 in Bbb Z_5 = Bbb Z / (5) tag 2$
means that
$x in 3 + (5), tag 3$
that is,
$x - 3 = 5n, ; n in Bbb Z, tag 4$
i.e.,
$x equiv 3 pmod 5. tag 5$
If I were grading the test I would accept either notation as correct.
edited Dec 10 '18 at 3:12
Bill Dubuque
208k29190628
answered Dec 10 '18 at 1:22
Robert Lewis
43.7k22963
add a comment |
If one accepts that
$Bbb Z / (5) equiv Bbb Z_5, tag 1$
then it is evident that
$x = 3 in Bbb Z_5 = Bbb Z / (5) tag 2$
means that
$x in 3 + (5), tag 3$
that is,
$x - 3 = 5n, ; n in Bbb Z, tag 4$
i.e.,
$x equiv 3 pmod 5. tag 5$
If I were grading the test I would accept either notation as correct.
edited Dec 10 '18 at 3:12
Bill Dubuque
208k29190628
answered Dec 10 '18 at 1:22
Robert Lewis
43.7k22963
If one accepts that
$Bbb Z / (5) equiv Bbb Z_5, tag 1$
then it is evident that
$x = 3 in Bbb Z_5 = Bbb Z / (5) tag 2$
means that
$x in 3 + (5), tag 3$
that is,
$x - 3 = 5n, ; n in Bbb Z, tag 4$
i.e.,
$x equiv 3 pmod 5. tag 5$
If I were grading the test I would accept either notation as correct.
edited Dec 10 '18 at 3:12
Bill Dubuque
208k29190628
answered Dec 10 '18 at 1:22
Robert Lewis
43.7k22963
edited Dec 10 '18 at 3:12
Bill Dubuque
208k29190628
edited Dec 10 '18 at 3:12
Bill Dubuque
208k29190628
edited Dec 10 '18 at 3:12
Bill Dubuque
208k29190628
208k29190628
answered Dec 10 '18 at 1:22
Robert Lewis
43.7k22963
answered Dec 10 '18 at 1:22
Robert Lewis
43.7k22963
answered Dec 10 '18 at 1:22
Robert Lewis
43.7k22963
43.7k22963
add a comment |
add a comment |
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1
Yes. ${}{}{}{}$
– YiFan
Dec 10 '18 at 1:25
@WillFisher The correct notation is the OP's $ xequiv 3pmod 5. $ Your notation $ xequiv 3mod 5,$ is not correct and often causes beginners to confuse relational vs. operational mod.
– Bill Dubuque
Dec 10 '18 at 3:11