Mixing
Showing $Theta_{i}$ defined on $prod _{iin I}mathcal{A}_{i}$ is a congruence relation.
0
$begingroup$
I am trying to use the previously asked question to help me finish my question. But I have a simple question about their "case 1" (when $a = b$). Why is it that if $a=b$, then $f(a)=f(b)$? Is this by definition or is it assumed f is well-defined? Thanks in advance.
universal-algebra congruence-relations
asked Jan 22 at 17:57
numericalorangenumericalorange
1,775311
$endgroup$
add a comment |
0
$begingroup$
I am trying to use the previously asked question to help me finish my question. But I have a simple question about their "case 1" (when $a = b$). Why is it that if $a=b$, then $f(a)=f(b)$? Is this by definition or is it assumed f is well-defined? Thanks in advance.
universal-algebra congruence-relations
asked Jan 22 at 17:57
numericalorangenumericalorange
1,775311
$endgroup$
3
$begingroup$
Well $f$ is function, right ?
$endgroup$
– user626177
Jan 22 at 18:21
1
$begingroup$
@someone You're right! Totally forgot such a trivial definition. This really shows that as one studies mathematics, some simple concepts can be forgotten at moments like this!
$endgroup$
– numericalorange
Jan 22 at 18:33
1
$begingroup$
It would be unnatural not to forget anything, but the only thing that matters is to understand things well!
$endgroup$
– user626177
Jan 22 at 18:39
add a comment |
0
0
0
$begingroup$
I am trying to use the previously asked question to help me finish my question. But I have a simple question about their "case 1" (when $a = b$). Why is it that if $a=b$, then $f(a)=f(b)$? Is this by definition or is it assumed f is well-defined? Thanks in advance.
universal-algebra congruence-relations
asked Jan 22 at 17:57
numericalorangenumericalorange
1,775311
$endgroup$
I am trying to use the previously asked question to help me finish my question. But I have a simple question about their "case 1" (when $a = b$). Why is it that if $a=b$, then $f(a)=f(b)$? Is this by definition or is it assumed f is well-defined? Thanks in advance.
universal-algebra congruence-relations
universal-algebra congruence-relations
asked Jan 22 at 17:57
numericalorangenumericalorange
1,775311
asked Jan 22 at 17:57
numericalorangenumericalorange
1,775311
asked Jan 22 at 17:57
numericalorangenumericalorange
1,775311
asked Jan 22 at 17:57
numericalorangenumericalorange
1,775311
asked Jan 22 at 17:57
numericalorangenumericalorange
1,775311
1,775311
3
$begingroup$
Well $f$ is function, right ?
$endgroup$
– user626177
Jan 22 at 18:21
1
$begingroup$
@someone You're right! Totally forgot such a trivial definition. This really shows that as one studies mathematics, some simple concepts can be forgotten at moments like this!
$endgroup$
– numericalorange
Jan 22 at 18:33
1
$begingroup$
It would be unnatural not to forget anything, but the only thing that matters is to understand things well!
$endgroup$
– user626177
Jan 22 at 18:39
add a comment |
3
$begingroup$
Well $f$ is function, right ?
$endgroup$
– user626177
Jan 22 at 18:21
1
$begingroup$
@someone You're right! Totally forgot such a trivial definition. This really shows that as one studies mathematics, some simple concepts can be forgotten at moments like this!
$endgroup$
– numericalorange
Jan 22 at 18:33
1
$begingroup$
It would be unnatural not to forget anything, but the only thing that matters is to understand things well!
$endgroup$
– user626177
Jan 22 at 18:39
3
3
$begingroup$
Well $f$ is function, right ?
$endgroup$
– user626177
Jan 22 at 18:21
$begingroup$
Well $f$ is function, right ?
$endgroup$
– user626177
Jan 22 at 18:21
1
1
$begingroup$
@someone You're right! Totally forgot such a trivial definition. This really shows that as one studies mathematics, some simple concepts can be forgotten at moments like this!
$endgroup$
– numericalorange
Jan 22 at 18:33
$begingroup$
@someone You're right! Totally forgot such a trivial definition. This really shows that as one studies mathematics, some simple concepts can be forgotten at moments like this!
$endgroup$
– numericalorange
Jan 22 at 18:33
1
1
$begingroup$
It would be unnatural not to forget anything, but the only thing that matters is to understand things well!
$endgroup$
– user626177
Jan 22 at 18:39
$begingroup$
It would be unnatural not to forget anything, but the only thing that matters is to understand things well!
$endgroup$
– user626177
Jan 22 at 18:39
add a comment |
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3
$begingroup$
Well $f$ is function, right ?
$endgroup$
– user626177
Jan 22 at 18:21
1
$begingroup$
@someone You're right! Totally forgot such a trivial definition. This really shows that as one studies mathematics, some simple concepts can be forgotten at moments like this!
$endgroup$
– numericalorange
Jan 22 at 18:33
1
$begingroup$
It would be unnatural not to forget anything, but the only thing that matters is to understand things well!
$endgroup$
– user626177
Jan 22 at 18:39