Journal of Formalized Mathematics
Volume 1, 1989
University of Bialystok
Copyright (c) 1989 Association of Mizar Users

## Some Properties of Real Numbers Operations: min, max, square, and square root

Andrzej Trybulec
Warsaw University, Bialystok
Czeslaw Bylinski
Warsaw University, Bialystok

### Summary.

We define the following operations on real numbers: $max(x,y)$, $min(x,y)$, $x^2$, $\sqrt{x}$. We prove basic properties of introduced operations. A number of auxiliary theorems absent in [2] and [3] is proved.

Supported by RPBP.III-24.C1.

#### MML Identifier: SQUARE_1

The terminology and notation used in this paper have been introduced in the following articles [4] [6] [1] [5] [3]

Contents (PDF format)

#### Bibliography

[1] Grzegorz Bancerek. The ordinal numbers. Journal of Formalized Mathematics, 1, 1989.
[2] Krzysztof Hryniewiecki. Basic properties of real numbers. Journal of Formalized Mathematics, 1, 1989.
[3] Jan Popiolek. Some properties of functions modul and signum. Journal of Formalized Mathematics, 1, 1989.
[4] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[5] Andrzej Trybulec. Subsets of real numbers. Journal of Formalized Mathematics, Addenda, 2003.
[6] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.