Give an example of a function ....

In summary, a function that is periodic, non-constant, and has no minimal period can be represented by f(x) = 0, where x is a rational number. This is discussed in the last paragraph of the Examples section in the Wikipedia article on periodic functions.
  • #1
alexmahone
304
0
Give an example of a function which is periodic, non-constant, and yet has no minimal period.
 
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  • #2
Read the Wikipedia article on periodic functions.
 
  • #3
Evgeny.Makarov said:
Read the Wikipedia article on periodic functions.

I know what a periodic function is and I read the Wikipedia article. Yet, I cannot answer the question.
 
  • #4
But it gives an example you are looking for in the last paragraph of the Examples section.
 
  • #5
Evgeny.Makarov said:
But it gives an example you are looking for in the last paragraph of the Examples section.

Thanks.
 
  • #6
Since you appear to already have the answer, let f(x) be any non-continuous function satisfying f(1)= 0 and f(x+y)= f(x)+ f(y). That will be periodic with every rational number as period.
 

FAQ: Give an example of a function ....

What is a function in science?

A function in science is a mathematical relationship between two or more variables, where the value of one variable is dependent on the value of another variable. It can also refer to a process or operation that produces a specific output based on a given input.

Can you provide an example of a function in science?

Sure, an example of a function in science could be the relationship between force and acceleration, where force is the input and acceleration is the output. This can be represented by the equation F=ma, where m is mass and a is acceleration.

How are functions used in scientific research?

Functions are used in scientific research to model and analyze complex systems, make predictions, and understand the relationship between different variables. They are also used to create mathematical models that can be tested and validated through experiments and observations.

Are there different types of functions in science?

Yes, there are different types of functions in science, including linear, quadratic, exponential, logarithmic, and trigonometric functions. Each type has its own unique characteristics and uses in scientific research and applications.

Can functions be applied to non-mathematical concepts in science?

Yes, functions can also be applied to non-mathematical concepts in science, such as in biology where enzymes can be described as functions that catalyze biochemical reactions in living organisms. They can also be used to describe relationships in fields like ecology, sociology, and economics.

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