Math Is Fun Forum

PatternMan

Member

Registered: 2014-03-08

Posts: 199

Why is there an associative law?

I mean I understand the commutative law but why is there even an associative law? It's just there are only addition operations and the commutative law which allows you to ignore the precedence rule of parenthesis. Well that's how I always thought of it.

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"School conditions you to reject your own judgement and experiences. The facts are in the textbook. Memorize and follow the rules. What they don't tell you is the people that discovered the facts and wrote the textbooks are people like you and me."

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Why is there an associative law?

It needs to be a formal rule because there non-associative operations.

The commutative law does not allow omitting parentheses.

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

Isomorph

Member

Registered: 2014-06-19

Posts: 5

Re: Why is there an associative law?

Hello again anonimnystefy, and hello PatternMan.

I've just started to learn Latex so perhaps I could practise it by adding here the formula for the number of ways that n numbers can be combined to illustrate the Associative Law:

(The brackets denote a binomial coefficient).

A couple of examples:

With n=3 numbers (1,2,3) there are 2 ways to associate them:

1. (1 + 2) + 3
2.  1 + (2 + 3)

With n=4 numbers (1,2,3,4) there are 5 ways to associate them:

1. 1 x (2 x (3 x 4))
2. 1 x ((2 x 3) x 4)
3. (1 x 2) x (3 x 4)
4. ((1 x 2) x 3) x 4
5. (1 x (2 x 3)) x 4

Last edited by Isomorph (2014-06-23 11:24:40)

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Why is there an associative law?

Hi Isomorph

What does that have to do with why there is an associative law?

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

Isomorph

Member

Registered: 2014-06-19

Posts: 5

Re: Why is there an associative law?

Hi anonimnystefy,

Nothing at all. Your answer to PatternMan's question was perfect.

The subject put me in mind of that nesting formula, and so I took the opportunity to try Latex out (I've just read the crash course in the index). Sorry for any confusion

(It's occurred to me that my 2nd sentence was ambiguous. I didn't mean that the formula itself illustrates the associative law; I meant that it counts the ways of 'bracketing' up numbers that people use when they want to illustrate the associative law. I can see how that was misleading - oops!)

Last edited by Isomorph (2014-06-23 12:46:02)

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Why is there an associative law?

Oh, sorry. It's not exactly perfect, but it is wglhat it is.

I see you know about the Catalan numbers.

Also, congrats for learning LaTeX. Tip: you can use \binom{}{} for the binomial coefficient.

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.