What Does It Mean for a Function to Be Single Valued?

[Hermes10]

Hello,

I was doing problem involving Fourier Series and came across the Dirichlet conditions which say among others that the function has to be single valued in order to be able to use Fourier Series to describe it.

What does it mean for a function to be single valued?


Hermes10

 

[mathman]

It means what it says. y=f(x) is single-valued if given an x, there is only one y.

An example which is not is f(x) = square root of x, which is double valued.

 

[eumyang]

An example which is not is f(x) = square root of x, which is double valued.

This isn't true. The square root function of a positive real number is defined to be always positive.

This is different from solving equations involving square roots. For example, if x² = 4, then there are two solutions: √4 = 2, or -√4 = -2.

 

[mathman]

This isn't true. The square root function of a positive real number is defined to be always positive.

This is different from solving equations involving square roots. For example, if x² = 4, then there are two solutions: √4 = 2, or -√4 = -2.

Nitpicker!

 

[Stephen Tashi]

"Multivalued functions" are to "functions" as "counterfeit money" is to "money".