Why is there so much emphasis on whether osomething is a function

[johnqwertyful]

I was tutoring someone for an intro mathematical logic class and there were a few problems about proving something is a function or not. I remember in high school algebra, there were a pretty large emphasis on the vertical line test. In precalculus I saw it again. In calculus I saw it again. In this intro to logic course there was proving that something was a function.

Why does it even matter? After intro to logic I have never really seen a reason why we even care. The only place where it even matters is in complex analysis when you have to define branch cuts for multivalued functions. But it really wasn't that big of a deal, and most people who take high school algebra won't see complex analysis. I could kind of see in a logic class, as an example of proof. But it seems strange that after that class, I have never seen it come up again really. In math or physics or science or anything really.

 

[olivermsun]

I was tutoring someone for an intro mathematical logic class and there were a few problems about proving something is a function or not...Why does it even matter? After intro to logic I have never really seen a reason why we even care. The only place where it even matters is in complex analysis when you have to define branch cuts for multivalued functions. But it really wasn't that big of a deal, and most people who take high school algebra won't see complex analysis. I could kind of see in a logic class, as an example of proof. But it seems strange that after that class, I have never seen it come up again really. In math or physics or science or anything really.

You never see circles, hyperbolas, shocks?

 

[johnqwertyful]

I see them all the time.

 

[olivermsun]

So you know they're not described by functions.
It's just one of those things—you learn it once and hopefully you know to recognize and/or avoid problems that arise from it.
That's how I tend to view the relevance of function/not function for the general audience anyway.

 

[johnqwertyful]

Yes, I agree they're not described by functions. But that's never really mattered, there's never really been a problem. I mean maybe a tiny bit, but it seems like there was a ton of emphasis. I've seen it in multiple classes.

 

[olivermsun]

Yes, I agree they're not described by functions. But that's never really mattered, there's never really been a problem. I mean maybe a tiny bit, but it seems like there was a ton of emphasis. I've seen it in multiple classes.

Yeah, I don't know. It's a huge problem in differential equations—when the solution goes "non function." Doubt that's of much relevance to the majority of students though.

I do agree with you that it seems to receive a lot of time, despite being a pretty simple concept to understand (and test in most cases).

 

[symbolipoint]

Having nothing more than just a feeling for the answer, a function giving exactly one output for anyone input is an important distinction to make. This points to inversability.

 

[olivermsun]

Good point.

 

[HallsofIvy]

We like questions that have one correct answer! When scientist do an experiment repeatedly, it is important that they get the same result each time. A "function" models that property.