And, remind ourselves that a mapping connects two sets by establishing pairs. For example the mapping f:A → B, might create the pairs (a,, bą), (a2, b2). (a3. b3), and so on. This pairs each element in A with some element in B. We also know that some mappings between sets are onto, one-to-one or both. You might also note that if we can establish a 1-1 correspondence (onto and one-to-one) between A and B, then we would know the sets were equal. (Can either of explain why?) As we shift to thinking about a group, we have an operation to consider and some special things that have to happen. In other words, in order for the mapping to show the groups are structurally the same (a version of equal), the mapping has to ensure key elements to each other and it has to preserve the operation. What key elements would we want to map to one another? What would have to be true if operation *A in A works in essentially the same way operation *B Works in B?

And, remind ourselves that a mapping connects two sets by establishing pairs. For example the mapping f:A → B, might create the pairs (a,, bą), (a2, b2). (a3. b3), and so on. This pairs each element in A with some element in B. We also know that some mappings between sets are onto, one-to-one or both. You might also note that if we can establish a 1-1 correspondence (onto and one-to-one) between A and B, then we would know the sets were equal. (Can either of explain why?) As we shift to thinking about a group, we have an operation to consider and some special things that have to happen. In other words, in order for the mapping to show the groups are structurally the same (a version of equal), the mapping has to ensure key elements to each other and it has to preserve the operation. What key elements would we want to map to one another? What would have to be true if operation A in A works in essentially the same way operation B Works in B?

Name: Please help with this discussion: And, remind ourselves that a mapping
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Description: Please help with this discussion: And, remind ourselves that a mapping connects two sets by establishing pairs. For example, the mapping \( f: A \rightarrow B \), might create the pairs \((a_1, b_1), (a_2, b_2), (a_3, b_3)\), and so on. This pairs ea

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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