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Question 65819: I'm sorry that this question isn't on this topic, but i couldn't find another topic for my question, and anyway this topic is the most closely related to my question.
My question is about the "closure property". in the newest barrons review book, the blue one {for the ny regents}, it says on page 8 that real numbers only have this closure property for addition and multiplacation. My problem is why doesn't subtraction and division also have this closure property. please show me examples to tillustrate.
happy new year
nathan
Answer by funmath(2933)   (Show Source):
You can put this solution on YOUR website! Hi Nathan,
The closure propterty for addition and multiplication states that:
If a and b are real numbers, then a+b and ab are real numbers.
I haven't thought of a reason that it may not apply to subtraction, but I immediately thought of the fact that 0 is a real number, but anything divided by 0 is undefined and does not result in a real number.
Hope that helps.
Happy Calculating, Nathan!!!
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