Journal of Formalized Mathematics
Volume 2, 1990
University of Bialystok
Copyright (c) 1990
Association of Mizar Users
Factorial and Newton Coefficients

Rafal Kwiatek

Nicolaus Copernicus University, Torun

Supported by RPBP.III24.B5.
Summary.

We define the following functions: exponential function (for natural
exponent), factorial function and Newton coefficients. We prove
some basic properties of notions introduced.
There is also a proof of binominal
formula. We prove also that $\sum_{k=0}^n {n \choose k}=2^n$.
MML Identifier:
NEWTON
The terminology and notation used in this paper have been
introduced in the following articles
[9]
[2]
[3]
[10]
[8]
[5]
[4]
[6]
[1]
[7]
Contents (PDF format)
Bibliography
 [1]
Grzegorz Bancerek.
The fundamental properties of natural numbers.
Journal of Formalized Mathematics,
1, 1989.
 [2]
Grzegorz Bancerek.
The ordinal numbers.
Journal of Formalized Mathematics,
1, 1989.
 [3]
Grzegorz Bancerek.
Sequences of ordinal numbers.
Journal of Formalized Mathematics,
1, 1989.
 [4]
Grzegorz Bancerek and Krzysztof Hryniewiecki.
Segments of natural numbers and finite sequences.
Journal of Formalized Mathematics,
1, 1989.
 [5]
Czeslaw Bylinski.
Functions and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
 [6]
Czeslaw Bylinski.
Finite sequences and tuples of elements of a nonempty sets.
Journal of Formalized Mathematics,
2, 1990.
 [7]
Czeslaw Bylinski.
The sum and product of finite sequences of real numbers.
Journal of Formalized Mathematics,
2, 1990.
 [8]
Krzysztof Hryniewiecki.
Basic properties of real numbers.
Journal of Formalized Mathematics,
1, 1989.
 [9]
Andrzej Trybulec.
Tarski Grothendieck set theory.
Journal of Formalized Mathematics,
Axiomatics, 1989.
 [10]
Andrzej Trybulec.
Subsets of real numbers.
Journal of Formalized Mathematics,
Addenda, 2003.
Received July 27, 1990
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