Math Is Fun Forum

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Properties of Real Numbers...Part 4

Distributive Properties

a (b + c) = ab + ac

(a + b) c = ac + bc

Why is this property considered one of the most important in mathematics?

Identity Properties

Let n be a number.

0 + n = n + 0 = n

n • 1 = 1 • n = n

Does this property also work for subtraction and division?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,637

Re: Properties of Real Numbers...Part 4

I've no idea why the questioner thinks it's more important. Most number analysis would fall apart if any axiom were dropped

1/n is not n.  1 - n is not n so the identity property doesn't hold.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Properties of Real Numbers...Part 4

I've no idea why the questioner thinks it's more important. Most number analysis would fall apart if any axiom were dropped

1/n is not n.  1 - n is not n so the identity property doesn't hold.

Bob

Can it be that perhaps distributive properties are often needed to remove parentheses, a skill often ignored by students?