Math / Algebra

Questioname the Field Axiom that was use $x+(y+z)=(x+y)+z$

Studdy Solution

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.

STEP 7

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

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Questioname the Field Axiom that was use $x+(y+z)=(x+y)+z$

Studdy Solution

STEP 1

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.

STEP 7

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

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Questioname the Field Axiom that was use x+(y+z)=(x+y)+zx+(y+z)=(x+y)+zx+(y+z)=(x+y)+z

Studdy Solution

STEP 1

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)+zx + (y + z) = (x + y) + zx+(y+z)=(x+y)+z, shows that it doesn't matter how we **group** numbers when we add them.Adding xxx to the sum of yyy and zzz gives the same result as adding the sum of xxx and yyy to zzz.

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.

STEP 7

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

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Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Questioname the Field Axiom that was use $x+(y+z)=(x+y)+z$

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

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!

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.

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 $z$ .

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.