Subset: a set contained in a set

Two weeks ago, we have talked about the basics of sets.  In this post, we are going to talk about subsets.

If you understand what this means, then you have a notion of a subset.

In mathematics, if $A$ and $B$ are sets, we say that $A$ is a subset of $B$, denoted by $A \subseteq B$, if all elements of $A$ are also elements of $B$. The easiest way to illustrate this is through a Venn diagram as shown on the right.  In the Venn diagram, set $A$ is within set $B$. Therefore, all elements of set $A$ are also elements of $B$.

Example 1

Let$B$ be set of all letters in the English alphabet and $A$ be the set of vowel letters. It is clear that $A \subseteq B$ since {aeiou} are elements $A$ and also are elements of $B$. » Read more

The Peanut Math Software Package

If you have enjoyed learning GeoGebra, Compass and Ruler, Geometer’s Sketchpad, and Wolfram Alpha, and other  free math software, you might want to check out the Peanut Math Software package from Philip Exeter University. Some software included in the package also include games and puzzles. The package includes the following software:

• Wingeom –  for high-precision geometric constructions in both two and three dimensions
• Winplot – a general-purpose plotting utility, which can draw (and animate) curves and surfaces presented in a variety of formats.
• Winstats – provides access to scatter plots, curve fitting, histograms, statistical data, and standard theoretical probability distributions. It performs many statistical tests and calculates confidence intervals. It simulates dealing cards, rolling dice, sampling candy, taking random walks, and tossing darts, needles and coins
• Winarc – a collection of game subprograms, currently including Life, Krypto, Boxes, Hex, Rubik, Mazes, Pegs, Bishops, the Loyd 15 puzzle, Spaceship, and Sudoku
• Winfeed –  a fractal exploration program. It allows the user to explore functional iteration, including Mandelbrot and Julia sets, ferns and snowflakes, web and bifurcation diagrams, and more.
• Windisc – a collection of subprograms that deal with discrete-math topics such as apportionment, voting power, voting methods, bin-packing, and network analysis (traveling salesman problem, map-coloring, etc).
• Winmat –  allows the user to calculate and edit matrices, and solve standard linear algebra problems. The program operates in real, complex, and integer mode.
• Wincalc – allows the user to calculate integers with millions of digits.
• Winwordy –  a collection of word puzzles.