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"On the set of ℝ suppose operation * is defined by a * b = 1 + ab. Is * a binary operation?"

 

This question is confusing. I get to see addition right there, yet the variables a and b are multiplied. I don't know what operation the * stands for.

 Sep 9, 2018
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your confusion comes from seeing * and thinking ordinary multiplication.

 

In this problem it's not.

 

think of * in this case as *(a,b) = 1 + ab where a and b are mutliplied using ordinary real multiplication

 

for example 2*5 = 1 + (2)(5) = 11

 

* takes two real arguments and returns a real result so yes it is a binary operator on the real numbers

 Sep 9, 2018

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