#Inverse proportional?

255 messages · Page 1 of 1 (latest)

lavish sleetBOT
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rockhoven

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pale dragon
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I've never seen notation like this. Can you provide context?

hallow parrot
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yes I have to search

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OK someone said that it is best to think of fractions like this. Does that make sense with the formula?

pale dragon
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Oh. Then it's just division, I guess.

hallow parrot
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ok it's an inversion of multiplication

pale dragon
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Yeah, definitely division, then.

hallow parrot
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I'm asking you i

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I don't know what it is

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$a\times^{-1}b$

lavish sleetBOT
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rockhoven

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pale dragon
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It's just a/b.

hallow parrot
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someone said to think of fractions like this

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ok

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because I want to think of 2/3 like this

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but I would think it easier to just invert to 3/2

pale dragon
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I think the point of this is to show that a/b = ab^(-1).

hallow parrot
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how does this work with 2/3?

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let me try it

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-1 x 3 = -3

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-3 x 2 = -6

sleek flower
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Well in terms of algebraic structure that’s how division should be defined a x b^-1 =a/b the right side of the equality is a notation

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( if b is nonzero of course so it’s invertible)

hallow parrot
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what is ^

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?

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so this is not an inverse proportional?

pale dragon
hallow parrot
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I have no idea

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why do we need a power?

pale dragon
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That's just a basic property of powers: 1/b = b^(-1).

hallow parrot
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2/3 is both a fraction and a division

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it's the same thing

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sort of

sleek flower
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It’s a definition if you are in a ring ( or field in this case) the inverse of b (if invertible) is written b^-1

hallow parrot
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in whole number math a smaller number is not divisible by a larger number

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that's all i know is whole number math

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the poster said it is best to think of fractions in this form

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$a\times^{-1}b$

lavish sleetBOT
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rockhoven

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hallow parrot
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So how would we think of 2/3?

sleek flower
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If you are writing « 2/3 » you aren’t doing arithmetic if that’s what you mean we are in (R,+,x) which is a field and 2/3 is actually 2 x 3^-1 ( 1/3 is the inverse of 3)

hallow parrot
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so it is an inverse proportion?

sleek flower
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Well if you define X^-1 :(a,b)—> a X^-1 b=a x b^-1 then I guess yes

hallow parrot
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2/3 is actually 2 x 3^-1

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you are pulling my leg now?

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X^-1 :(a,b)—> a X^-1 b=a x b^-1

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what is that?

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2/3?

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well that second one is a general statement?

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2/3 is actually 2 x 3^-1
?

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why is it necessary to use a power?

sleek flower
hallow parrot
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ok

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let's see

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the power along with -1 makes an inversion?

sleek flower
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b^-1=1/b

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( for a non zero b )

hallow parrot
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then this is simply an inverse proportional?

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right

sleek flower
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I guess yes

hallow parrot
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because 0/1 iand 1/0 are not inverse proportionals?

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ok

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then why not just say "inverse proportional"?

pale dragon
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What even is an inverse proportional?

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I've never heard of that term.

hallow parrot
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LOL

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2/3 ∝ 3/2

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that's all

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that's all I know

pale dragon
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Maybe you meant (2/3)^(-1) = 3/2?

hallow parrot
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I may not know how to use ∝

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you are not using ∝ at all

pale dragon
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Why would we use it when talking about just numbers?

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Proportionality is useful when talking about variables, not just numbers.

hallow parrot
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we have the same idea but it's another vocabulary

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ok

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I don't know very much

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but the poster said that it's best to think of fractions using this formula

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i don't know why it would be any more beneficial over just saying "inverse proportional"

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or using ∝

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fractions consist of numbers

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so that is the context

pale dragon
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I mean, to me a/b just means ab^(-1).

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That's just it, really.

hallow parrot
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where did you learn this?

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I have no modern math skills

pale dragon
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In middle school, I guess.

hallow parrot
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only classical math

pale dragon
hallow parrot
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whole number math in which 1 is indivisible

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not quite

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there is a difference in classical thinking about numbers

pale dragon
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What exactly do you mean by "classical"?

hallow parrot
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pre modern

pale dragon
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And what is "modern"?

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You have to be more precise.

hallow parrot
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at some point 1 became dividible

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no clear line of demarcation

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in plato's and euclid's time 1 was indivisible

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it makes for some controversy

pale dragon
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Wait, you mean you started learning mathematics by reading ancient texts?

hallow parrot
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yes

pale dragon
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Uhh... well, I mean, they are interesting, sure. But I don't think that's a good idea.

hallow parrot
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well

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I am not a mathematician

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and don't intend to become one

pale dragon
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I mean, this is just arithmetics. This is what you learn in middle school.

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Doesn't matter whether you want to be a mathematician or not, everyone learns this.

hallow parrot
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I didn't go to school

pale dragon
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Wait, what?

hallow parrot
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8th grade educatuon over here

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education

pale dragon
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But that means you did go to school.

hallow parrot
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ok

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i spose

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i also went to college

pale dragon
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If you're in 8th grade, this should all be familiar to you from long ago.

hallow parrot
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I went to a college and looked at it and left

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so i went to college

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$a\times^{-1}b$

lavish sleetBOT
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rockhoven

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hallow parrot
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anyway someone else is telling me that this is meaningless

pale dragon
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Well, this just means that division and multiplication are inverse operations.

hallow parrot
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i dont get it

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yes

pale dragon
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Noone really writes it like this, of course.

hallow parrot
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but you just said that

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and i understnd that

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i could hhave told you that

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it must be some conventional shorthand for the phrase

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it's needed for doing more than just fractions

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variables

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so this sort of has something to do with inverse proportionals but not necessarily so?

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can it be used any other way

pale dragon
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Sorry, but I have no idea what you're talking about.

hallow parrot
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how would it be different if we were using variables

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it would still represent an inverse realtion

pale dragon
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But we are using variables here: a and b.

hallow parrot
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relation

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a/b ∝ b/a

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this produces square relations

pale dragon
hallow parrot
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ok

pale dragon
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Ah, although...

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Let's see.
a/b = k(b/a)
a^2 = kb^2
So, this means that a ~ b.

hallow parrot
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a is similar to b

pale dragon
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No, I mean that a is proportional to b.

hallow parrot
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I shoud hope so

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if they have square relation they are similar

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both the sides and the areas are proportional

pale dragon
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Variables can be proportional, not similar. Shapes can be similar.

hallow parrot
fallow surge
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why did you make a discussion post about this

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ok i accept that this notation may have been a goofy step off the beaten path that confused everyone

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i was indeed just trying to say that a fraction is something that undoes multiplication

sleek flower
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Fr il quite confused tbh

fallow surge
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in a way that does not use the concept of an inverse element

pale dragon
hallow parrot
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I think we should go back to using an indivisible 1

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***i was indeed just trying to say that a fraction is something that undoes multiplication

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I understand that

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but I learned that by working with inverse proportionals

fallow surge
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great good for you

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guess i have to be careful in the future not to say anything that might trigger anyone to unleash another discussion post on this poor forum

hallow parrot
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I don't think there's any problem

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I'm doing fine

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I love it

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It's great

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We are here to have a good time and pick up a bit of knowledge here and there

hallow parrot
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I don't think that we can disassociate math from prose

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Since math is a language, there has to be explanations for what is said

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Einstein writes in prose while introducing his formulas and equations

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The symbols of math are symbols for ideas

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The underlying ideas are what matters

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once we agree upon the ideas then mathematical symbols can be applied

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for example

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in this conversation we could represent my whole last sentence by the letter a

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the a is all I have to write in order to express that statement

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a = "once we agree upon the ideas then mathematical symbols can be applied"

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The main reason for using one letter is to abbreviate waht we are saying

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instead of writing out 10 or 12 words every time we wanted to refer to our topic we could just write one letter a

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but it is the ideas that matter here

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maybe you will counter and say that is logic, not math

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let b = "I'll have some pumkin pie"

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what is a/b?

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"once we agree upon the ideas then mathematical symbols can be applied" / "I'll have some pumkin pie" ?

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This does not make any sense

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and the reason is that these two things are not homogenous

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you can't divide mathemtical symbols by pumkin pie

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they are heterogeneous terms

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and substances

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Let Q.E.D = So There!

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Q.E.D.

hallow parrot
# fallow surge i was indeed just trying to say that a fraction is something that undoes multipl...

I am trying to be as agreeable as I can be. I just want clarity. Nothing is expressed poorly if we can agree upon it. I just want to know what it means before I sign on to.it. I uncritically accpted 1 + 1 = 2 when I was 6 years old and I shouldn't have. "i was indeed just trying to say that a fraction is something that undoes multiplication" OK. So I'll agree to the that. That is something I have continued to learn by working with inverse proportionals. I'm just wondering how I can understand and utilize this formula. That depends on whetehr I can input numbers and get the desired outputs. Your formula need only be tested and possibly refined. I wouldn't know. I am not a mathematician. Most of us here are dummies. Run some tests on your formula and give us some demonstrations that we can understand. I don't think that you have made any misstep in attempting to formulate a thought. All ask is that you continue.

prisma remnant
hallow parrot
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When fishing for an idea, you wrote something. Now you think it's goofy?

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That is usually the sign of intuition. You may have had a bunch of math lurking around in your brain.

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and it spontaneously erupted. Such thought are initially going to appear ridiculous to you conscious mind

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however you may just be on the right track

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I reward you with a song. Keep the ideas coming

hallow parrot
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Why can't we thinkof 2/3 as -6. What other number could we expect to come out of the formula? A prime? 11? No. I would expect 6 to come out because 2 and 3 went into the forumla. I think it is also an inverse proportional because it carries a negative sign, it produced -6. I really think you may have hit upon something. All we haev to do now is give the formula some extra meaning which elucidates the thought processes.

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Now, -6*6=-36

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6 has to be able to represent 2/3 because we set up the internal structure of the number to be so. There undoubtedly is a relation between 2/3 and 6.

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Now inverse ratios look like this: 3:2 ∝ 2:3 and such a relation generates squares which is what has occurred here. for the extremes of this proportion are square 3x3 and the means are square 2x2 which gives a square relation of 4 to 9. 4 and 9 are factors of 36. Your equation spits out -6 and -6x6=-36, yet another square. -6 and 6 must be representative of our original inverse ratio of 3:2 ∝ 2:3 .

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The fact that the relations are square numbers indicates an inverse proportional.

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But I am even more interested in the intuitive processes that brought this to your mind and those intuitive processes that led me to a recognition of your genius.

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I said before that I sometimes played with relations (ratios) of two or more numbers in my mind. Just very low numbers and elementary mathematical thinking. I more than once noticed that if I played with these number long enough I ended up with whole numbers. Your formula renders whole numbers. You also said in introducing the formula that this is the way to think about fractions. I intuitively agree with you but I don't yet know why. That is why I am instigating a full review of your formula to find out what makes it work and how we thought this thing up together directly from the subconscious materials of math.

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Remember - it's the thought that matters

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Now how did you think up this formula? Surely it has some history?

hallow parrot
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You know it just dawns on me that we are all saying the same thing no matter the language of math that we speak, no matter what your equations are or how you write them, we are all talking about proportion

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that's it

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that's really all there is to the math business

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proportionals

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all of this different math that you and I do or don't understand is about proportionals

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when you talk about Maxwell's spectrum or Pascal's triangle or a Fouier series

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it's all about proportion

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trig calc all of it

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I mean I don't know that stuff but that is my guess

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I want to say this because there may be some confusions in the way we are communicating

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but we are all talking about this same thing in different ways

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what the formula in the OP comes down to is proportion

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because it was admitted to express a proportion, namely, a fraction

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I put a ratio into

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all that could come out of it was a ratio or a proportion

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because that is what I put into it

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so the output of -6 from the forumla must simply be accepted and understood as expressing a proportion

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I put 2/3 into it

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why should any number other than 6 come out of it?

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-6 is just an inverse relation

sleek flower
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Well in a mathematical group the inverse of an element b is denoted b^-1 so if you consider (R,+) it’s a group and « 3^-1 » is « -3 » for that group but that’s a notation when we write 2/3 we of course are referring to the inverse of multiplication and not the inverse of addition because that’s just the way it was created and it makes sense

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Saying 2/3=-6 can make sense if you really stretch it like this but it’s a notation

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It’s like saying a cat and a dog are the same because both have four legs both have the same « property » they have both four legs ( in this case both are inverse in their respective sets, so group and field respectively) but that doesn’t mean they are the same that makes no sense

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My example is very bad but I hope it makes sense

sour bear
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If my grandmother had wheels she would be a bike

sleek flower
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That was bad

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My bad

hallow parrot
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LOL

hallow parrot
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but yes when I did stumble upon a whole number while thinking of fractions or comparisons of number or proportional, I did scratch my head and wonder how I arrived at a whole number. I know that saying that 6 can represent 2/3 may seem odd and it seemed odd to me then

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but I was wondering if an formula like this, if explored, could reveal what those thought processes were because if those processes are beneficial I would want to continue explorations there and if not I would want to be able to instantly recognize them and eliminate them.

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I am just wonding if this formula might be useful

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I rather like the idea of a whole number representing a relation between two numers

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because it's a crazy idea and I am not shy at all about handling strange ideas

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Einstein handled weird ideas for his time

hallow parrot
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I am now obsessed with this formula and these ideas

gleaming smelt
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How about $a +^{-1} b$? Or would it be $a (-1)+ b$?

lavish sleetBOT
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Djake3tooth

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