Talk:Abstract Algebra/Group Theory/Meaning of Diagrams in This Section

=Concepts that Need Representations=

For all and there exists

 * The filled circles are a good example for "for all"; do we need one for "there exists" ?

an element that may or may not be in a group

 * how about a filled circle that is on the edge of the round rectangle? Arydye001 (talk) 22:03, 26 July 2010 (UTC)

Inverse

 * an empty circle with thick rim and same colour to represent inverse of a filled circle
 * What if the filled circle has one inverse in one group and a different inverse on the other group?
 * We could use the color of the group to represent the inverse. For example, the rim for the original element and the filled color for the group..
 * Actually we don't need to specify a colour for the group because inverse of an element and the element must be within the same group.
 * What if an element and its inverse are both in two groups and the inverse is only under one of the group?
 * May be we can put the operator of a group on the groups' round rectangle, that will till that the inverse is due to which group.


 * What if the filled circle has one inverse for one operator and an other one for another operator?
 * hmm, now that is a problemArydye001 (talk) 22:03, 26 July 2010 (UTC)
 * May be we can put the symbol of the operator next to the circle to show that this is the inverse of such and such under this operator.
 * Symbols.... are they bad?
 * Not if you don't use them excessively. Arydye001 (talk) 22:21, 26 July 2010 (UTC)


 * What if the red circle has one red rimmed inverse in one group and then the red rimmed inverse has another inverse in another group?
 * Can we add another rim, like a red rimmed red rimmed circle?
 * Then is our first circle a red rimmed red rimmed red rimmed circle, and our 2nd circle both a red rimmed circle and a red rimmed red rimmed red rimmed red rimmed circle?
 * Is the empty circle a bad idea? Alternatively, we can use a special kind of lines linking the inverse and its element under some symbols to show that they are inverse to each other under some group and some operator?
 * May be we can combine the two ideas, we can use the red rimmed red rimmed circles and the lines together.

modular arithmetic
=Are Straight Lines Bad?=
 * They surely hide other possibilities. Straight lines make people think the elements and operators can only be connected in certain way.
 * A perspective is both informative and biased. Arydye001 (talk) 15:52, 30 July 2010 (UTC)