Math Snap

STEP 1

What is this asking?
Which of the field axioms is shown by the equation $x + (y + z) = (x + y) + z$?
Watch out!
Don't confuse the associative property of addition with the commutative property of addition ($x + y = y + x$) or the distributive property ($a \cdot (b + c) = a \cdot b + a \cdot c$).

STEP 2

1. Recall the field axioms.
2. Identify the relevant axiom.

STEP 3

Let's refresh our memory on the field axioms!
Remember, field axioms are fundamental rules that govern how numbers in a field behave under addition and multiplication.
They're like the basic building blocks of arithmetic!

STEP 4

There are quite a few axioms, including associativity, commutativity, identity elements, inverses, and the distributive property.
We're looking for the one that matches the given equation.

STEP 5

The given equation, $x + (y + z) = (x + y) + z$, shows that it doesn't matter how we group numbers when we add them.
Adding $x$ to the sum of $y$ and $z$ gives the same result as adding the sum of $x$ and $y$ to $z$.

STEP 6

This is precisely the definition of the associative property of addition!
It tells us that we can rearrange the parentheses in an addition problem without changing the outcome.

The field axiom demonstrated by the equation $x + (y + z) = (x + y) + z$ is the associative property of addition.