The Definition of a Group!!! Come to the talk today!!!!! Statistics Val 103 3:30 – 4:15.

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Presentation transcript:

The Definition of a Group!!!

Come to the talk today!!!!! Statistics Val 103 3:30 – 4:15

Can you use your transmitter? A. Yes B. No

Is ( ℝ +, +) a group? (a) Yes (b) No

Is (Z +, +) a group? (a) Yes (b) No

Why is (Z +, +) not a group? (a) I have no idea. What the heck is a group? (b) + is not a binary operation on this set (c) + is not associative (d) There is no identity (and hence no inverses) (e) There are no inverses (f) All of the above (except (a))

Is ( ℝ - {0},  ) a group? (a) Yes (b) No

Is ( ℝ, *) with a *b = 2(a+b) a group? (a) Yes. (b) No: * is not a binary operation on this set (c) No: * is not associative (d) No: There is no identity (and hence no inverses) (e) No: There are no inverses

What is entry A in the matrix multiplication: ( a) 1 (b) -2(c) 5 (d) 11(e) 13 (f) 0

What is entry D in the matrix multiplication: ( a) 1 (b) -2(c) 5 (d) 11(e) 13 (f) 0