Statement about factorials that I don't understand

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In summary, factorials are mathematical operations that multiply a number by all of the numbers below it. They are commonly used in scientific research, particularly in statistical analysis and probability calculations. While they can be useful, they may have limitations in accuracy and difficulty with larger numbers.
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Ertosthnes
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I was reading and came across this statement:

If t > 2n^2 is an integer, then t! > (n^2)^(t-n^2)

I'm not sure why it is true. I don't know what equations are relevant. My feeling is that you don't need anything more than algebra, but perhaps it would also follow from the gamma function or stirling's formula. Can anyone help me out?
 
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Have you tried to prove it by induction?
 

What is a factorial?

A factorial is a mathematical operation that multiplies a number by all of the numbers below it. For example, the factorial of 5 is 5x4x3x2x1=120.

How do factorials relate to scientific research?

Factorials are often used in statistical analysis to calculate the number of possible combinations or permutations of a given set of data. This helps researchers make predictions and draw conclusions from their data.

What is the significance of factorials in probability?

In probability, factorials are used to calculate the number of possible outcomes in a given situation. This allows researchers to determine the likelihood of a certain event occurring.

What is the difference between a factorial and a permutation?

A factorial is the product of a number and all the numbers below it, while a permutation is a specific arrangement of a set of items. Factorials are used to calculate the number of possible permutations.

Are there any limitations to using factorials in scientific research?

While factorials can be useful in certain situations, they can become very large and difficult to calculate with larger numbers. Additionally, they may not accurately represent real-world scenarios and should be used with caution.

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