Logic Question

[chaosCG]

So in many non-Math realms, I often find that people attempt to incorporate mathematical concepts into subjects but often are hazy at best when asked to explain it out.

(*an ambiguous statement, I know, let me give you an example)​

I'll pose this logic question to all of you experts out there:

In higher education healthcare, the terms "inversely proportional" and "directly proportional" are used many times over, usually to discus some physics law that is being applied to physiology.

Many look like this.
i.e.:​

A = B/C​

The statement is made that A is inversely proportional to C,
therefore; as C increases, A decreases and as C decreases, A increases.​

(as long as C is greater than or equal to 1) ***Correction: as long as C > 0 *****​

However.....

what if the equation looked like this:
​

A = B - C
?????????
​

It is STILL true that as as C increases, A decreases and as C decreases, A increases
​

​

is A still inversely proportional to C?
Why? or Why not?

​

Thanks in advance for anyone willing to tackle this question that is probably much to simple for this category.

~Chris (ChaosCG)

 

[Dr.Peterson]

So in many non-Math realms, I often find that people attempt to incorporate mathematical concepts into subjects but often are hazy at best when asked to explain it out.

(*an ambiguous statement, I know, let me give you an example)​

I'll pose this logic question to all of you experts out there:

In higher education healthcare, the terms "inversely proportional" and "directly proportional" are used many times over, usually to discus some physics law that is being applied to physiology.

Many look like this.
i.e.:​

A = B/C​

The statement is made that A is inversely proportional to C,
therefore; as C increases, A decreases and as C decreases, A increases.​

(as long as C is greater than or equal to 1, a point never mentioned in healthcare academia)​

Actually, that condition is not required; if C increases from 1/4 to 1/2 (doubling), A decreases (halving). The restriction is that all numbers are assumed to be positive.

However.....

what if the equation looked like this:
​

A = B - C
?????????
​

It is STILL true that as as C increases, A decreases and as C decreases, A increases
​

(and this time there are no limitations to this statement as there was in the previous equation)​

So,​

is A still inversely proportional to C?
Why? or Why not?

​

Thanks in advance for anyone willing to tackle this question that is probably much to simple for this category.

~Chris (ChaosCG)

A is not inversely proportional to C, simply because it doesn't fit the definition.

What definition are you using for "inversely proportional"?

 

[Steven G]

So in many non-Math realms, I often find that people attempt to incorporate mathematical concepts into subjects but often are hazy at best when asked to explain it out.

(*an ambiguous statement, I know, let me give you an example)​

I'll pose this logic question to all of you experts out there:

In higher education healthcare, the terms "inversely proportional" and "directly proportional" are used many times over, usually to discus some physics law that is being applied to physiology.

Many look like this.
i.e.:​

A = B/C​

The statement is made that A is inversely proportional to C,
therefore; as C increases, A decreases and as C decreases, A increases.​

(as long as C is greater than or equal to 1, a point never mentioned in healthcare academia)​

However.....

what if the equation looked like this:
​

A = B - C
?????????
​

It is STILL true that as as C increases, A decreases and as C decreases, A increases
​

(and this time there are no limitations to this statement as there was in the previous equation)
​

So,
​

is A still inversely proportional to C?
Why? or Why not?

​

Thanks in advance for anyone willing to tackle this question that is probably much to simple for this category.

~Chris (ChaosCG)

I agree with It is STILL true that as as C increases, A decreases and as C decreases, A increases

​

Is A still inversely proportional to C?? That depends on your definition of inversely proportional. I (and anyone I know) do not use that definition. We use A is inversely proportional to C if (ie iff) A = K/C for some constant K
​

 

[chaosCG]

Actually, that condition is not required; if C increases from 1/4 to 1/2 (doubling), A decreases (halving). The restriction is that all numbers are assumed to be positive.



A is not inversely proportional to C, simply because it doesn't fit the definition.

What definition are you using for "inversely proportional"?

Hah, I work with Healthcare Professionals and Healthcare Educators, most of who have two common qualities about them:

​

1) They were never Math majors (nor did they want to be)
2) They are almost ALL Type A so telling them they are wrong, regardless of the topic, is often not worth the hassle.
​

The most recent example that comes to mind was involving a lecture on Transpleural Pressures relation to Alveolar Pressures. The equation is so simple (TPP = AP - IP) but to hear a graduate professor, of all people, suggest that TPP is "inversely proportional to IP because as IP increases, TPP decreases," well it just made my skin crawl listening to her "educate" other soon-to-be healthcare providers on this concept.

That being said, I admittedly felt a little silly asking this question. But it is used so often to simply (and at times incorrectly) express a relationship that "as one value increases, the another decrease", that I wanted to make sure that I didn't have a misunderstanding of the application of the terms or concept before I said anything.

Thanks for the feedback.
~Chris

 

[JeffM]

So in many non-Math realms, I often find that people attempt to incorporate mathematical concepts into subjects but often are hazy at best when asked to explain it out.

(*an ambiguous statement, I know, let me give you an example)​

I'll pose this logic question to all of you experts out there:

In higher education healthcare, the terms "inversely proportional" and "directly proportional" are used many times over, usually to discus some physics law that is being applied to physiology.

Many look like this.
i.e.:​

A = B/C​

The statement is made that A is inversely proportional to C,
therefore; as C increases, A decreases and as C decreases, A increases.​

(as long as C is greater than or equal to 1, a point never mentioned in healthcare academia) WHAT ARE YOU TALKING ABOUT?​

However.....

what if the equation looked like this:
​

A = B - C
?????????
​

It is STILL true that as as C increases, A decreases and as C decreases, A increases
​

(and this time there are no limitations to this statement as there was in the previous equation)​

So,​

is A still inversely proportional to C?
Why? or Why not?

​

Thanks in advance for anyone willing to tackle this question that is probably much to simple for this category.

~Chris (ChaosCG)

First, what is higher education healthcare? There is no doubt that the educational system is a mess, but has it been hospitalized?

Second, I agree that many people use mathematical terms incorrectly in an attempt to provide a false impression of precision. But in most cases, this is done out of carelessness or ignorance rather intentional deceit. Saying "inverse proportion" when what is meant is an "inverse relation" or a "negative correlation" is hardly the worst such mistake I have heard.

Third, the mathematical definition of "inverse proportion" is

\(\displaystyle x \text { and } y \text { are inversely proportional if and only if there exists } a \ne 0 \text { such that } x = \dfrac{a}{y}.\)

Don't take my word for it.

https://en.m.wikipedia.org/wiki/Proportionality_(mathematics)

So obviously \(\displaystyle x = a - y\) does not fit the mathematical definition of inverse proportionality.

Fourth, consider \(\displaystyle x = \dfrac{10}{y}.\)

You agree, I hope, that one quarter of a pie is less than one half of a pie.

So if y goes from 1/4 to 1/2, y is increasing.

\(\displaystyle x = \dfrac{10}{\dfrac{1}{4}} \implies \dfrac{1}{4} * x = 10 \implies x = 40.\)

\(\displaystyle x = \dfrac{10}{\dfrac{1}{2}} \implies \dfrac{1}{2} * x = 10 \implies x = 20.\)

As the example shows, if y increases, x decreases even though y < 1.

 

[Dr.Peterson]

Hah, I work with Healthcare Professionals and Healthcare Educators, most of who have two common qualities about them:

1) They were never Math majors (nor did they want to be)
2) They are almost ALL Type A so telling them they are wrong, regardless of the topic, is often not worth the hassle.
​

The most recent example that comes to mind was involving a lecture on Transpleural Pressures relation to Alveolar Pressures. The equation is so simple (TPP = AP - IP) but to hear a graduate professor, of all people, suggest that TPP is "inversely proportional to IP because as IP increases, TPP decreases," well it just made my skin crawl listening to her "educate" other soon-to-be healthcare providers on this concept.

That being said, I admittedly felt a little silly asking this question. But it is used so often to simply (and at times incorrectly) express a relationship that "as one value increases, the another decrease", that I wanted to make sure that I didn't have a misunderstanding of the application of the terms or concept before I said anything.

Thanks for the feedback.
~Chris

If the context were mathematical (say, they were about to do a calculation based on the proportionality statement, and didn't already have the equation), then they would be fully wrong.

As it is, they are just misusing language. They mean to say "inversely related"; and what they mean is correct, though their words are not. It's a minor infraction in this context, just using the wrong word to describe the right relationship.

So, yes, you are right about the meaning of "inversely proportional"; but it is really only the word "proportional" that is wrong, while "inversely" is not.

 

[chaosCG]

First, what is higher education healthcare? There is no doubt that the educational system is a mess, but has it been hospitalized?

An excellent example of why it is important to re-read one's post before posting them to a form of experts. Yes, "higher education healthcare" is an odd and inaccurate attempt to express that I was referring to a medically focused graduate program... good catch.

Second, I agree that many people use mathematical terms incorrectly in an attempt to provide a false impression of precision. But in most cases, this is done out of carelessness or ignorance rather intentional deceit. Saying "inverse proportion" when what is meant is an "inverse relation" or a "negative correlation" is hardly the worst such mistake I have heard.
...

This is actually exactly what I was looking for - "inverse relation" or a "negative correlation" - I knew "inversely proportional" was inaccurate but I didn't know how to express it otherwise.

...
You agree, I hope, that one quarter of a pie is less than one half of a pie.
...

Totally agree with you here also, a half of a pie is waaaaaaay gooder than a quarter of one.

Another excellent example of why re-reading one's post is vital prior to clicking that submit button.

Thanks again!

~Chris

 

[topsquark]

Hah, I work with Healthcare Professionals and Healthcare Educators, most of who have two common qualities about them:

1) They were never Math majors (nor did they want to be)
2) They are almost ALL Type A so telling them they are wrong, regardless of the topic, is often not worth the hassle.
​

Unfortunately it's not just the non-Mathematically minded people that do this.

I once toured North Carolina University to see about completing my PhD and I listened outside the door of a professor that was lambasting her student about the fact that he didn't know that 0/0 = 1. When he slumped out the doorway I went in for my appointment and made the mistake of asking if 0/0 = 1 was a new convention because as far as I knew it was undefined. I got a five minute lecture about how I needed to take remedial Math classes if I were to attend one of her lectures.

-Dan

 

[Steven G]

Unfortunately it's not just the non-Mathematically minded people that do this.

I once toured North Carolina University to see about completing my PhD and I listened outside the door of a professor that was lambasting her student about the fact that he didn't know that 0/0 = 1. When he slumped out the doorway I went in for my appointment and made the mistake of asking if 0/0 = 1 was a new convention because as far as I knew it was undefined. I got a five minute lecture about how I needed to take remedial Math classes if I were to attend one of her lectures.

-Dan

That is simply amazing. Just to confirm this professor had a PhD in math?

 

[topsquark]

That is simply amazing. Just to confirm this professor had a PhD in math?

She's a pre-eminent String Theorist. I'll be polite and not mention the name.

-Dan

 

[pka]

Unfortunately it's not just the non-Mathematically minded people that do this.
I once toured North Carolina University to see about completing my PhD and I listened outside the door of a professor that was lambasting her student about the fact that he didn't know that 0/0 = 1. When he slumped out the doorway I went in for my appointment and made the mistake of asking if 0/0 = 1 was a new convention because as far as I knew it was undefined. I got a five minute lecture about how I needed to take remedial Math classes if I were to attend one of her lectures.
-Dan

Dan, that is inscrutable story. I have great familiarity with UNC. UNC along with UVA are considered the two southern "Public-Ivys".
Please tell me your appointment was not with anyone in mathematics, not even a graduate assistant.

 

[tkhunny]

Dan, that is inscrutable story. I have great familiarity with UNC. UNC along with UVA are considered the two southern "Public-Ivys".
Please tell me your appointment was not with anyone in mathematics, not even a graduate assistant.

In the programming world, someone must decide what to do when a program encounters 0/0. In some languages, 0/0 = 1, by default. If you do not want this result, you must control the engagement. In some languages, it is NaN. Some may call it 0. Some simply spit out an error. Perhaps this nameless Professor was working on a large programming project that week - in a language where 0/0 = 1.

 

[topsquark]

Dan, that is inscrutable story. I have great familiarity with UNC. UNC along with UVA are considered the two southern "Public-Ivys".
Please tell me your appointment was not with anyone in mathematics, not even a graduate assistant.

Not a Math Professor. Physics. But even in String Theory, even with some of the weird Math involved, 0/0 is still indeterminate. (Yeah, there's 1 + 2 + 3 + ... = -1/12, but there's at least a fig leaf to hide behind for that one.) I am not saying she's a bad Physicist or Mathematician, just wrong in this instance and not willing to hear anything to the contrary.

-Dan

 

[jtayag0622]

I agree with It is STILL true that as as C increases, A decreases and as C decreases, A increases

​

Is A still inversely proportional to C?? That depends on your definition of inversely proportional. I (and anyone I know) do not use that definition. We use A is inversely proportional to C if (ie iff) A = K/C for some constant K
​

true... I also use inversely proportional/varies inversely in cases like proportions or variations, not in A=B-C

 

[JeffM]

Unfortunately it's not just the non-Mathematically minded people that do this.

I once toured North Carolina University to see about completing my PhD and I listened outside the door of a professor that was lambasting her student about the fact that he didn't know that 0/0 = 1. When he slumped out the doorway I went in for my appointment and made the mistake of asking if 0/0 = 1 was a new convention because as far as I knew it was undefined. I got a five minute lecture about how I needed to take remedial Math classes if I were to attend one of her lectures.

-Dan

That story is so depressing that, as consolation, I am going to blow my diet by having an Armagnac and chocolates.

 

[Steven G]

She's a pre-eminent String Theorist. I'll be polite and not mention the name.

-Dan

I know that some people on here are Physicists but this really goes to show that Physicists are different people from most. A strong arithmetic student knows that 0/0 is indetermined but a String Theorist does not. WOW.

 

[jtayag0622]

I know that some people on here are Physicists but this really goes to show that Physicists are different people from most. A strong arithmetic student knows that 0/0 is indetermined but a String Theorist does not. WOW.

am not really sure how to feel about this but I'm starting to like your math skills dude. why bother discuss 0/0 when it's obvious. you're absolutely right Jomo.