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**(-infinity,infinity)****Member**- Registered: 2012-10-11
- Posts: 6

Hi,

I am currently in Alg 2 and was thinking if there was a logical way, preferably in proof format, that would prove that math is indeed fun. It would be great to show my classmates and teachers, but I haven't been able to come up with anything.

Any method of proofs would work, and I am thinking an indirect proof or proof by contradiction would work the best.

Thanks

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi (-infinity,infinity);

Welcome to the forum! A proof that math is fun, hmmmm....

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**zetafunc.****Guest**

Interesting idea with the proof by contradiction. "Let's assume that maths isn't fun..."

**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,407

hi (-infinity,infinity)

Welcome to the forum.

All proofs require a set of axioms and rules for how elements may be combined.

Here's a simple example.

axiom 1. All 4 lettered words are fun.

rules of propositional calculus apply.

normal counting rules apply.

proof. math has 4 letters (by counting rule)

math is fun (by axiom 1)

Now I'm not seriously offering this as a useful mathematical theory. I have two main objections:

(i) the proof breaks down in the UK where the spelling is 'maths'

note the extra 's' in the address.

(ii) There are a lot of 4 lettered words that you wouldn't want to be proved to be fun!

So clearly more work is needed on the axioms, but it will give you the idea.

btw. proof by contradiction still uses the axiom system and rules of logic.

Bob

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

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,407

OK. I have a better one.

Words have meanings. Dictionaries define those meanings.

So I chased around the definitions thus:

fun: bringing pleasure

doing something for pleasure: something you do because you want to rather than because you have to.

Now the proof.

We all know that 2 + 2 = 4

Only a mathematician would do the following:

axiom 1. 2 = 1 + 1

axiom 2. 3 = 2 + 1

axiom 3. 4 = 3 + 1

rules of substitution apply

associativity applies

proof:

2 + 2 = 2 + (1 + 1) (by substitution and axiom 1)

= (2 + 1) + 1 (associativity)

= 3 + 1 (substitution and axiom 2)

= 4 (substitution and axiom 4)

therefore 2 + 2 = 4

Only a mathematician would do this because they want to (clearly you don't have to do this)

Therefore math(s) is fun.

QED.

Bob

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

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**(-infinity,infinity)****Member**- Registered: 2012-10-11
- Posts: 6

Great thinking guys! I never thought of using the actual meaning of fun in the proof.

The warm welcome was also well appreciated.

I'll see if there are any other ideas, but bob bundy's looks like the best one so far.

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,407

hi (-infinity,infinity)

I'm surprised that you didn't think the meaning of a word was important.

Just to keep my suggestion in 'best' position I have improved it a little.

definition:

definition:

definition:

Let x = {devising the following proof}

axiom 1. 2 = 1 + 1

axiom 2. 3 = 2 + 1

axiom 3. 4 = 3 + 1

rules of substitution apply

associativity applies

proof:

2 + 2 = 2 + (1 + 1) (by substitution and axiom 1)

= (2 + 1) + 1 (associativity)

= 3 + 1 (substitution and axiom 2)

= 4 (substitution and axiom 4)

therefore 2 + 2 = 4

It is self evident that

Hope you like this.

Bob

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

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,039

Hi Bob

That's cool. Another contribution to our real world mathematics formulas. I think Real's friends will like it.

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.

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,407

hi

Just adding some more. Go back to post 7

B

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,407

Ok I'm done for now. See post 7.

I see you have given (-infinity,infinity) a nickname.

B

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,039

bob bundy wrote:

It is self evident that

And why is that?

bob bundy wrote:

I see you have given (-infinity,infinity) a nickname.

Yup!

*Last edited by anonimnystefy (2012-10-12 07:54:13)*

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.

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**(-infinity,infinity)****Member**- Registered: 2012-10-11
- Posts: 6

I see anonimnystefy has caught onto the interval notation.

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,039

Hi Real

It would be hard not to!

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.

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,407

It is self evident that

I have gone to some length to prove that 2 + 2 = 4

Ask any 4 year old and they will tell you it was not necessary to prove this ... "Don't be silly; everyone knows this!"

Therefore I must have been doing something that is "an activity not in {compulsory activities}"

It follows that it must be in {pleasurable activities}.

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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Hmm... Funny Posts ... Great

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,407

Hmm... Funny Posts ... Great

Which is further supportive evidence of the proposition that .....

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**(-infinity,infinity)****Member**- Registered: 2012-10-11
- Posts: 6

Bob, you have inspired me to get back to proofs. Thank you so much!

I removed that last part for privacy reason.

*Last edited by (-infinity,infinity) (2012-10-14 15:21:25)*

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,407

OK. Good luck with that.

For years mathematicians have found it difficult to get law courts to understand Bayes theorem and use it properly in assessing evidence where probability plays a part so you may have even more trouble pursuading them to accept your stalker proof.

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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