I’ve just started to create apparel for Sententias. The general theme of the clothing and accessories will be philosophy, theology, and science. I just started it today and there will be plenty of more to come. In the near future I will have all the designs that are currently in male shirts on female shirts, an organization of apparel by topic, and, of course, more options. Please share this with your friends! If you have any ideas or suggestions please leave it in the comment section. You can always access the store via the Apparel tab at the top. Here are a few samples:

## Information Theory

Information theory is the branch of probability theory that deals with uncertainty, accuracy, and information content in the transmission of messages. It can be applied to any system of communication (electric signals, fiber optic pulses, speech, etc.). Random signals, known as noise, are often added to a message during the transmission process, altering the signal received from that sent. Information theory is used to work out the probability that a particular signal received is the same as the signal sent. In transmitting a sequence of numbers, their sum might also be transmitted so that the receiver will know that there is an error when the sum does not correspond to the rest of the message. The sum itself gives no extra information, simply a confirmation. The statistics of choosing a message out of all possible messages (letters like the alphabet or binary digits for example) determines the amount of information contained in it. Information is measured in bits (binary digits). If one out of two possible signals are sent then the information content is one bit. A choice of one out of four possible signals contains more information although the signal itself might be the same.

For more information see John Daintith and John Clark’s *The Facts on File Dictionary of Mathematics* (New York: Market Book House, 1999), 97.

## Mathematical Induction

A method of proving mathematical theorems, used particularly for series sums. For example, it is possible to show that the series 1 + 2 + 3 + 4 + … has a sum of *n *terms of *n*(*n* + 1)/2. Firest one must show that if it is true for *n* terms it must also be true for (*n* + 1) terms. According to the formula

*S _{n}* =

*n*(

*n*+ 1)/2

if the formula is correct, the sum of (*n* +1) terms is obtained by adding (*n *+1) terms is obtained by adding (*n* + 1) to this

*S _{n+}*

_{1}=

*n*(

*n*+ 1)/2 + (

*n*+1)

*S _{n+}*

_{1}=

*n*(

*n*+ 1)(

*n*+ 2)/2

This agrees with the result obtained by replacing *n* in the general formula by (*n* + 1), i.e.:

*S _{n+}*

_{1}=

*n*(

*n*+ 1)(

*n*+ 1 + 1)/2

*S _{n+}*

_{1}=

*n*(

*n*+ 1)(

*n*+ 2)/2