Quick question about asymptotic growth

Dragonfall · 2009-06-15T06:53:58+00:00

(\lg n)!\in\mathcal{O}((\lg n)^{\lg n}) right?

Thread starter Dragonfall
Start date Jun 15, 2009
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Growth

In summary, asymptotic growth is the behavior of a mathematical function as its input approaches a certain value. It can be measured using various methods and is influenced by factors such as initial conditions and external influences. It is commonly observed in real-life systems and is different from exponential growth in that it approaches a value rather than increasing indefinitely.

Jun 15, 2009

Dragonfall

[tex](\lg n)!\in\mathcal{O}((\lg n)^{\lg n})[/tex] right?

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Jun 15, 2009

CRGreathouse

Science Advisor

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Right, you can get that from Stirling's formula. (Assuming that either n is a power of 2 or you use gamma(lg(n) + 1), of course.)

Jun 15, 2009

Dragonfall

Excellent, thanks.

1. What is asymptotic growth?

Asymptotic growth refers to the behavior of a mathematical function as its input approaches a certain value. In the context of scientific research, it is often used to describe the growth of a population or the increase in a variable over time.

2. How is asymptotic growth measured?

Asymptotic growth can be measured using various mathematical methods, such as calculating the limit of a function as its input approaches a certain value, or using regression analysis to determine the best-fit curve for a set of data points.

3. What are the main factors that affect asymptotic growth?

The main factors that affect asymptotic growth can vary depending on the specific context, but generally include variables such as initial conditions, external influences, and the inherent properties of the system being studied.

4. Can asymptotic growth be observed in real-life systems?

Yes, asymptotic growth can be observed in many real-life systems, such as population growth, economic trends, and the spread of diseases. It is a common phenomenon in natural and social sciences and is often used to make predictions about future behavior.

5. How is asymptotic growth different from exponential growth?

While asymptotic growth and exponential growth may appear similar, they are fundamentally different concepts. Asymptotic growth describes the behavior of a function as it approaches a certain value, while exponential growth describes a constant rate of increase over time. Asymptotic growth can approach but never reach a specific value, while exponential growth continues to increase indefinitely.