0
$\begingroup$

I hope guys here don't judge people by their first question :)

For a naive, like me, I don't know what this problem formal name might be or even if this a worthy problem, but hopefully this won't deter anyone with knowledge from providing guidance.

Assuming we have the following quantities :

$$ x= a-b $$ $$ y= a-c $$ $$ z= b-c $$

is it possible to get an approximate estimation of any of $a, b, c$. Or perhaps get a formula where only one of them dominates ?

  • 0
    What do you mean by "a formula where only one of them dominates"? – 2017-02-22
  • 0
    @EricWofsey I don't have very specific thing in mind, but if I have, for example, $a^4+b-c$ , then $a$ has larger weight than the others, right? – 2017-02-22
  • 0
    Not if $a$ is small (like $0.01$); then it has almost no weight. But I want to respond to your initial point: this is *absolutely* a good question, and you asked it pretty well. There's no shame in not knowing the answer -- that's why we're here! (You don't need to use bold for the question, though -- we'll find it all by ourselves, by looking for the "?". :) One more thing: if you've played with a question a little bit, it's nice to also say "Here's what I've come up with so far" -- that lets us know something about your level of mathematical sophistication, so we can answer appropriately. – 2017-02-22

1 Answers 1

1

The numbers $x$, $y$, and $z$ alone do not allow you to even approximately determine any of the numbers $a$, $b$, and $c$. First, note that $x+z=(a-b)+(b-c)=a-c=y$, so $y$ tells you no information that $x$ and $z$ do not already tell you.

Now given values of $x$ and $z$, let $d$ be any number. If we define $c=d$, $b=d+z$ and $a=d+x+z$, notice that these three numbers will satisfy $x=a-b$ and $z=b-c$ (and also $y=a-c$ if $y=x+z$). So given the values of $x$ and $z$, $c$ could be any number at all (whatever we want to choose $d$ to be). Similarly, $a$ and $b$ could each also be any number at all by changing $d$.

So if you know $x$ and $z$, you can't say anything about any of the numbers $a$, $b$, and $c$ individually. You just know something about how they are related to each other (namely, what the differences between them are).