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.III-24.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 non-empty 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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