c/plain
... represent all numbers in binary (base 2). We (humans) often write numbers as decimal and hexadecimal for convenience, so need to be able to convert to binary and back (to understand what computer is doing!). Adding two 1-bit numbers generalizes to adding two numbers of any size since 1-bit full adde ...
... represent all numbers in binary (base 2). We (humans) often write numbers as decimal and hexadecimal for convenience, so need to be able to convert to binary and back (to understand what computer is doing!). Adding two 1-bit numbers generalizes to adding two numbers of any size since 1-bit full adde ...
Functions
... Show that (fg) is one-to-one if g:AB and f:BC are both one-to-one. Proof: We must show that, x,yA, xy (fg)(x) (fg)(y). Let x,y be distinct elements of A. Then, since g is one-to-one, g(x) g(y). Now, since g(x) g(y) and f is one-to-one, then f(g(x)) = (fg)(x) f(g(y)) = (fg)(y). ...
... Show that (fg) is one-to-one if g:AB and f:BC are both one-to-one. Proof: We must show that, x,yA, xy (fg)(x) (fg)(y). Let x,y be distinct elements of A. Then, since g is one-to-one, g(x) g(y). Now, since g(x) g(y) and f is one-to-one, then f(g(x)) = (fg)(x) f(g(y)) = (fg)(y). ...
1 Expectation of a discrete random variable
... not provide a complete information about the distribution. It is possible to have many different distributions with the same expectation. For example, suppose that in the example above the payoff is -2 when the outcome is odd and 2 when the outcome is even. The expected value of this distribution is ...
... not provide a complete information about the distribution. It is possible to have many different distributions with the same expectation. For example, suppose that in the example above the payoff is -2 when the outcome is odd and 2 when the outcome is even. The expected value of this distribution is ...
Elementary mathematics
Elementary mathematics consists of mathematics topics frequently taught at the primary or secondary school levels. The most basic topics in elementary mathematics are arithmetic and geometry. Beginning in the last decades of the 20th century, there has been an increased emphasis on problem solving. Elementary mathematics is used in everyday life in such activities as making change, cooking, buying and selling stock, and gambling. It is also an essential first step on the path to understanding science.In secondary school, the main topics in elementary mathematics are algebra and trigonometry. Calculus, even though it is often taught to advanced secondary school students, is usually considered college level mathematics.