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# Geometry/Factorial computations

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QUESTION: Dear Prof Azeem

http://en.wikipedia.org/wiki/Factorial

Can we use Factorials for various computations viz Addition, Subtraction,Multiplication,Division and indices ?.

Addition = 3! + 2!

Subtraction = 3! - 2!

Multiplication = 3! * 2!

Division = 3! / 2!

Exponential / Indices = 3! raised to a power of 2!

Other than the above computations, can we use Factorials in Matrices, Determinants, logarithms, Antilogarithms, Coordinate Geometry etc.

Matrices = 2*2 matrix = 3!,2!,5!,6!
Determinants = 3!,2!,5!,6!
Logarithms = log(10!), log(20!) etc
Antilogarithms = Antilog(1!) etc
Coordinate geometry = plot this points in the Graph paper viz
A(3!,2!), B(4!,-5!),C(-7!,-8!),D(6!,-3!)
Trigonometry = Sin(5!), Cos(4!), Tan(2!), Sec(3!), Cosec(6!), Cot(7!)

etc

Thanks & Regards,
Prashant S Akerkar

ANSWER: Hi Prashant,

To all the above, yes.  Factorials are integers, therefore they can be used wherever integers are used.

Thanks for asking,
Azeem

---------- FOLLOW-UP ----------

QUESTION: Dear Prof Azeem

Thanks.

Square root of 4!, Cube root of 7! etc

Thanks & Regards,
Prashant S Akerkar

Answer
Hi Prashant,

...That is not a question, but I can explain a bit.
All factorials are integers, so any operation that can be done with integers can be done with factorials.

For example, 4!=(4)(3)(2)(1)=24.
Therefore the square root of 4! is equal to the square root of 24.

Factorials are compact ways of expressing certain integers.  In all the contexts you have mentioned, it is a matter of notation, nothing further.

Regards,
Azeem

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#### Azeem Hussain

##### Expertise

I welcome your questions on algebra, 2D and 3D geometry, parabolic functions and conic sections, and any other mathematical queries you may have.

##### Experience

4 years as a drop-in and by-appointment tutor at Champlain College. Private tutor for dozens of clients over the past 8 years.

Publications
CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry

Education/Credentials
Bachelor of Science, Major Mathematics and Major Economics, McGill University, 2014. Diploma of Collegiate Studies; Pure and Applied Science, Champlain College Saint-Lambert, 2010.

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