Is Non-Periodicity Impossible in Functions?

  • Thread starter Fabio010
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In summary, a function is considered periodic if f(x+P) = f(x) for all x. However, if a function is not periodic, it is still possible for f(x+p) to be equal to f(x) for certain values of x.
  • #1
Fabio010
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Ok as we know, if f(x+P) = f(x) then the function is periodic.

So if the function is not periodic, f(x+p) = f(x) is a impossible equation right?
 
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  • #2
Fabio010 said:
Ok as we know, if f(x+P) = f(x) then the function is periodic.

So if the function is not periodic, f(x+p) = f(x) is a impossible equation right?

Nope. You forgot something in your first sentence about periodicity...
 
  • #3
If f(x+ p)= f(x) for all x then f is periodic. If f is NOT periodic, then there exist some x f(x+ p) is not the same as f(x). But there still might be many x for which that is true.
 

FAQ: Is Non-Periodicity Impossible in Functions?

What is periodicity?

Periodicity refers to the repeating pattern or cycle that occurs in a system or phenomenon. In science, this can refer to the recurrence of certain elements, properties, or behaviors at regular intervals.

What are some examples of periodicity in nature?

Examples of periodicity in nature include the cycles of the moon, the changing of seasons, the tides, and biological rhythms such as the circadian rhythm.

What is the periodic table?

The periodic table is a tabular display of the chemical elements, organized by their atomic structure and properties. It is a fundamental tool in chemistry and provides a systematic way to understand the relationships between different elements and their properties.

Why is periodicity important in science?

Periodicity is important in science because it allows us to predict and understand the behavior of natural phenomena. By identifying patterns and cycles, scientists can make predictions and develop theories to explain these patterns.

How is periodicity studied in science?

Periodicity is studied through various methods in science, such as observation, experimentation, and mathematical modeling. Scientists also use tools such as graphs, charts, and tables to visualize and analyze periodic patterns in data.

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