Is 'Find x' Really About Calculating the Value of x?

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In summary, a mathematician would expect the equation $x^2=4$ to be satisfied for the values of $x$ that are 2 and -2.
  • #1
I like Serena
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I was just wondering... my avatar is intended as a joke, but...

As I see it, mathematics is about being nitpicky.
That is, considering carefully what a question is, and answering exactly what was asked, not something unrelated, and not a long story that doesn't even contain the answer.
So if someone asks for which values of $x$ the equation $x^2=4$ is satisfied (within the context of the real numbers), I expect the answer $x=2$ and $x=-2$.
I don't expect a dissertation on algebra in general, nor do I expect that it's also possible that $y$ might be $3$.

If someone asks me to "find an apple", I might search for one, and point out where one is, which would be a geographic location.


verb (used with object), found, finding.
  1. to come upon by chance; meet with:
    He found a nickel in the street.
  2. to locate, attain, or obtain by search or effort:
    to find an apartment; to find happiness.
  3. to locate or recover (something lost or misplaced):
    I can't find my blue socks.
  4. to discover or perceive after consideration:
    to find something to be true.
  5. ...

Am I missing something?
Can "Find x" actually mean "Calculate the value of x"?

Or otherwise, how is it that in mathematics there are so many problems statements saying something like "Find x", when that is never what is intended?
It seems to me that "Find x" should be more related to treasure hunting, where the treasure is marked with an "x".
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  • #2
Meaning #4 is the pertinent one, here.
  • #3
Deveno said:
Meaning #4 is the pertinent one, here.

I'm guessing, since I'm not natively English speaking, that "find x" is a proper way to put the question.

Shouldn't it still be "find the value of x" then, or something like that?

In my own language, we use something that translates to "what is x" or "determine x".
  • #4
The intended meaning is: "discover which number $x$ is" (that is, assign it a value from the real numbers, or rational numbers, etc.).

The "joke" lies in conflating this with meaning #2: to locate.

This form of humor is called "deliberate misinterpretation", as in the following:

A programmer's wife asked her husband to go to the grocer's, "Get a loaf of bread. Oh, and if they have eggs, get a dozen".

He returned with 12 loaves of bread.
  • #5
My old math teacher had this rule he set himself.
Whenever his problem statement would be ambiguous, and people answered differently than intended, he would treat it as a correct answer.
This was sometimes abused, but he was very meticulous and kept himself objective.
He probably considered it his own fault for not being meticulously precise, which is what he was trying to instill on everyone.
And how could he do that, if he didn't set the example himself.

The other side was that if students were sloppy and/or wrote ambiguous answers, he would meticulously deduct 0.1 points - each and every time.
This doesn't sound like much, but if it happens about 50 times, it will guarantee an insufficient grade.
That happened to me when I first entered his class, which hit me hard at time, proud as I was of my math skills.
In retrospect, I've learned a lot from him, and after a while (it took about a year) my grades soared up higher than they were before.

I imagine that if he had phrased "find x" in one of his problem statements, and someone would answer with something like my avatar, he would smile grimly, and treat it as a correct answer.
Of course in any subsequent examinations there would never be a "find x" any more.

Related to Is 'Find x' Really About Calculating the Value of x?

1. What does "find x" mean in mathematics?

In mathematics, "x" is often used as a variable to represent an unknown value in an equation or problem. So, when someone says "find x", they are asking you to solve for the value of x.

2. Why is "x" used as a variable?

The use of "x" as a variable is a convention that dates back to the 17th century. It is believed to have been chosen because it is one of the last letters in the alphabet, and therefore represented an unknown or mysterious quantity.

3. How do you solve for "x"?

To solve for "x", you need to use algebraic methods to isolate the variable on one side of the equation. This typically involves using inverse operations, such as addition and subtraction, to cancel out any constants or coefficients that are attached to the variable.

4. Is "x" always the unknown value in an equation?

In most cases, "x" is used as the variable for an unknown value. However, it is possible for other letters to be used as variables as well, depending on the context of the problem. For example, in geometry, "a" and "b" are commonly used to represent side lengths of a triangle.

5. Are there any real-life applications of solving for "x"?

Yes, solving for "x" has many real-life applications in fields such as engineering, physics, and economics. For example, engineers may use algebraic equations to determine the optimal design for a bridge or building, while economists may use them to analyze supply and demand in a market.

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