Simple proof for arbitrary period

In summary, a simple proof for arbitrary period is a mathematical demonstration that shows the possibility of applying any given period to any set of numbers or values without restriction. This is important in establishing the concept of infinity and has practical applications in various fields. It differs from a regular proof in its focus on demonstrating the infinite nature of repeating patterns and uses a more abstract approach. An example of a simple proof for arbitrary period is the conversion of a repeating decimal to a fraction. The concept of arbitrary period can be applied in real-world situations such as computer algorithms, financial modeling, and problem-solving.
  • #1
zwoodrow
34
0
if f(t) has period T then f(kt) has a period T/k. What is a simple proof of this.
 
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  • #2
Why don't you just see what f(k(t+T/k)) is?
 

1. What is a simple proof for arbitrary period?

A simple proof for arbitrary period is a mathematical demonstration that shows that any given period, or repeating cycle, can be applied to any set of numbers or values. In other words, it proves that a repeating pattern can be applied infinitely and without restriction.

2. Why is proving arbitrary period important?

Proving arbitrary period is important because it helps to establish the concept of infinity and the idea that patterns can continue without end. It also has practical applications in various fields, such as computer science and engineering, where understanding and working with infinite patterns is necessary.

3. How is a simple proof for arbitrary period different from a regular proof?

A simple proof for arbitrary period specifically focuses on demonstrating that a repeating pattern can continue indefinitely, while a regular proof may not necessarily have this same focus. Additionally, a simple proof for arbitrary period often involves a more general and abstract approach to the proof, rather than specific examples or cases.

4. Can you provide an example of a simple proof for arbitrary period?

One example of a simple proof for arbitrary period is the proof that any repeating decimal can be converted into a fraction, such as 0.333... being equivalent to ⅓. This proof shows that the repeating pattern of the decimal can continue infinitely, without any restriction or limit.

5. How can the concept of arbitrary period be applied in real-world situations?

The concept of arbitrary period can be applied in various real-world situations, such as in creating computer algorithms or designing systems that require infinite patterns. It can also be used in financial modeling, where the idea of infinite patterns can help predict long-term trends and behaviors. Additionally, understanding arbitrary period can also aid in problem-solving and critical thinking skills.

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