Whole numbers and Other rational subjects

[OCTAVIA]

I was thinking alot about a solution to a question that I saw on the internet and I solved it, I wanted to ask the question; if a number like 3 is divisable by 3, the answer is 1, then if you add the next integer to it, you get the next number.

But, my question then went to this:

if you have an object that represents one whole thing and you divide it by another one whole thing then you have one; if you have two whole things and you divide it by two whole things then you should have two, not one. It seems the operation of division is viewed as being a simultaneous action. This makes it "rational". But if you take four beans for example and divide them by four equal beans, you would be dividing four beans four times. Not once. Can anyone explain the reason we get One for an answer?

[canthidefromme]

If you take 4 beans and divide by 4, you're dividing 4 beans by a unitless 4, not 4 beans by 4 beans, therefore you get 1 bean.
Now if you take 4 beans divided by 4 beans you get a unitless 1 (not 1 bean).

[Dave]

if you have 4 beans then you divide them by 4 people you get one bean per person.

Same with 4 beans divided by 4 beans you get one bean per bean.

[canthidefromme]

But can a bean really have a bean?

[Almightynoitall]

Originally posted by canthidefromme
But can a bean really have a bean?

Yes... case in point, Mr. Bean (Rowan Atkinson) likes Jelly beans... hence, if his family of four had four jelly beans to spilt amongst them, it'd be one bean per Bean... and vice versa... hehe.

[Almightynoitall]

Originally posted by OCTAVIA
if you have an object that represents one whole thing and you divide it by another one whole thing then you have one; if you have two whole things and you divide it by two whole things then you should have two, not one. It seems the operation of division is viewed as being a simultaneous action. This makes it "rational". But if you take four beans for example and divide them by four equal beans, you would be dividing four beans four times. Not once. Can anyone explain the reason we get One for an answer?

When you have multiple counters... and you are dividing them, think of it as sectioning things off... you have two beans, divide that by the 2, and you have one bean... PER SECTION. Now if you have two beans, and you divide it by bean, you can't remove the number, but the object... so you will have a meaningless two. Thus, logically, if you have two beans and divide it by that same two beans, you will cancel out the bean part, and have a meaningless two divided by a meaningless two, section two off into two parts and you'll have a meaningless 1.
Conclusioin: All math can lead to a meaningless answer!

[Iwant2bafencer]

Everything they've said in lamens terms: Yes math is stupid and has stupid rules, but unfortunately we still must take the classes and abide by the rules

I find the bean to a person the easiest way of explaining it like Dave said.
4people + 4 beans = 1 bean per person.

[Ramrod]

and... if too many people have too many beans, you have an empty room!

[canthidefromme]

Or if one person has too many beans

[Soldier]

Originally posted by Almightynoitall
Yes... case in point, Mr. Bean (Rowan Atkinson) likes Jelly beans... hence, if his family of four had four jelly beans to spilt amongst them, it'd be one bean per Bean... and vice versa... hehe.

Freshman and sophomore years, "Bean" was my nickname. One senior my freshman year said I looked like Rowan Atkinson, and nobody agreed, but the nickname stuck anyway. By sophomore year, nobody knew my real name anymore.

[Talysen]

Can one ever have too many beans?

I think not.

[OCTAVIA]

I know the deal, from my own math experience and I sort of decided to look at it a different way; in the sence that math, like any science has been 'rationalized' by people over the years, and because we all want good grades, so we buy into ideas. But, when you look at a number, any number it represents something: three "something" threenesses if you will. It theoretically stands for or represents one thing with 'threeness' quality, but did that idea just evolve? or did we really mean: 'three' which represents three things of this nature, which we will divide by three things of the SAME [?} nature or different nature [?}; will it make a difference? yes it does. It has to do with matching exactly.

4 pinto beans divided into 4 pinto beans if mashed into equal consistancy would equal one;
4 pinto beans that have their own separate nature and entity somehow get divided into 4 other pinto beans with the same nature is impossible, it would seem then that you would have to divide each bean individually making time part of this.

[Dave]

Buy a book on the philosophy and evolution of mathematics. There are lots out there some good and some unreadable.

IIRC it was one of the greeks who separated abstract numbers from those representing something directly but I haven't done any of this formally for a long time.

Most of the first semester of a maths degree is spent defining what is meant by a number (integer, rational, irational, neagative etc).

I have heard of lecture courses just about zero. The concept of zero is fundamental to the separation of the real and the abstract.

ps

IIRC it was one of the greeks who separated abstract numbers from those representing something directly but I haven't done any of this formally for a long time.

[OCTAVIA]

you're right Dave, and thanks. I almost lost my mind trying to work this out and it made no sence. My philosphy of math as it exists, is that it is so irrational that man just simply 'made it rational' for the sake of the universe, but I could be wrong. What would the universe be like under a different math system? What makes man count?