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Bashyboy Posted 12 years ago
Grammar
Mathematical Groups
Hello everyone,
I am trying to render my own definition of what a mathematical group is; in doing so, I have run into an ambiguity. Here is what I have thus far:
"A group is simply a set of objects * associated with some binary operator which acts on a pair of elements in G..."
I have used to a star to mark the place at which, I feel, ambiguity arises. The way it is written, the sentence seems to say that the binary operator is associated with the elements, and not with the set G as a whole. I would like to say that the binary operator is associated with the set as a whole. Would this wording seem to work better:
"A group G is simply a set of objects that is associated with some binary operator...."
I am trying to render my own definition of what a mathematical group is; in doing so, I have run into an ambiguity. Here is what I have thus far:
"A group is simply a set of objects * associated with some binary operator which acts on a pair of elements in G..."
I have used to a star to mark the place at which, I feel, ambiguity arises. The way it is written, the sentence seems to say that the binary operator is associated with the elements, and not with the set G as a whole. I would like to say that the binary operator is associated with the set as a whole. Would this wording seem to work better:
"A group G is simply a set of objects that is associated with some binary operator...."
Top answer
I don't see the ambiguity at ( *) since "binary operator" is qualified by "acting on a pair" The ambiguity is "a" which, to me, means, it can act on one pair of objects, not necessarily any pair-wise combination in the set. "A group, G, is a set of objects with (where there exists) some binary operator which acts on any pair of elements in G...
- I don't see the ambiguity at ( *) since "binary operator" is qualified by "acting on a pair" The ambiguity is "a" which, to me, means, it can act on one pair of objects, not necessarily any pair-wise combination in the set.
- "A group, G, is a set of objects with (where there exists) some binary operator which acts on any pair of elements in G...
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1 Answers
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I don't see the ambiguity at ( *) since "binary operator" is qualified by "acting on a pair"
The ambiguity is "a" which, to me, means, it can act on one pair of objects, not necessarily any pair-wise combination in the set.
"A group, G, is a set of objects with (where there exists) some binary operator which acts on any pair of elements in G...
The ambiguity is "a" which, to me, means, it can act on one pair of objects, not necessarily any pair-wise combination in the set.
"A group, G, is a set of objects with (where there exists) some binary operator which acts on any pair of elements in G...
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