- #1

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This is: Find a function f(x) of a variable x, x is in real field. the F(x) satisfy:

When x = 0, f(x) = 0

When x<>0, f(x) =1.

Anyone can help me?

Thank you.

- B
- Thread starter Viet Tu
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- #1

- 8

- 0

This is: Find a function f(x) of a variable x, x is in real field. the F(x) satisfy:

When x = 0, f(x) = 0

When x<>0, f(x) =1.

Anyone can help me?

Thank you.

- #2

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That appears to be a complete definition of the function. What more is there to find?

This is: Find a function f(x) of a variable x, x is in real field. the F(x) satisfy:

When x = 0, f(x) = 0

When x<>0, f(x) =1.

Anyone can help me?

Thank you.

Are you really asking whether it can be expressed in terms of standard functions?

Is this homework?

- #3

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Yes, it exactly is express form of function. It's not homework but created by myself when I solve a problem in my job.

- #4

jedishrfu

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My guess is you're trying to represent your function definition using common math functions in software where instead you could simply define a function to return a zero with x/=0 and a 1 when x=0.

This could be related to a Dirac Delta function (which really isn't a function):

https://en.wikipedia.org/wiki/Dirac_delta_function

where you could write it as something like this: ##f(x) = 1 - \delta(x)##

but of course this wouldn't work because ##\delta(x)## is infinite at x=0

- #5

Mark44

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Yes, we would like to see the scenario that this function describes.Perhaps you could describe the problem that came up at work.

Alternatively, the function could be defined piecewise.jedishrfu said:My guess is you're trying to represent your function definition using common math functions in software where instead you could simply define a function to return a zero with x/=0 and a 1 when x=0.

This could be related to a Dirac Delta function (which really isn't a function):

https://en.wikipedia.org/wiki/Dirac_delta_function

where you could write it as something like this: ##f(x) = 1 - \delta(x)##

but of course this wouldn't work because ##\delta(x)## is infinite at x=0

##f(x) = \begin{cases} 0 & \text{if }x = 0 \\ 1 & \text{if }x \ne 0 \end{cases}##

If this function is the result of a spreadsheet calculation, it's easy to build logic into a spreadsheet cell for this.

- #6

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Express it in what context? Are you writing a computer program? A spreadsheet formula? Or just a technical paper?

Yes, it exactly is express form of function. It's not homework but created by myself when I solve a problem in my job.

- #7

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Express as polynomial form. This is in spreadsheet formula. I have alternative solution, using "if" command. However, I'm trying to find a solution in math.Express it in what context? Are you writing a computer program? A spreadsheet formula? Or just a technical paper?

- #8

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No chance of polynomial form, or any "school" algebra. But don't think of math as limited to that. Math allows functions to be defined as you wrote it in post #1, and the appropriate way to express it in a spreadsheet is with IF.Express as polynomial form. This is in spreadsheet formula. I have alternative solution, using "if" command. However, I'm trying to find a solution in math.

- #9

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Thanks for your response.No chance of polynomial form, or any "school" algebra. But don't think of math as limited to that. Math allows functions to be defined as you wrote it in post #1, and the appropriate way to express it in a spreadsheet is with IF.

- #10

WWGD

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2019 Award

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How about ## 1- \chi_0 ## , where ##\chi_0 ## is the characteristic function of 0 , i.e. ##\chi_a## is 1 at a and 0 elsewhere ? EDIT : In my experience, most of the time, it is ##\chi_A ## , where ##A## is a set, but then you can just use ##A= ## {##a ##}

Last edited:

- #11

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I think it is a good solution. Nonetheless, it's too complicated for my case. Thank you so much.How about ## 1- \chi_0 ## , where ##\chi_0 ## is the characteristic function of 0 , i.e. ##\chi_a## is 1 at a and 0 elsewhere ? EDIT : In my experience, most of the time, it is ##\chi_A ## , where ##A## is a set, but then you can just use ##A= ## {##a ##}

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