Author Archives: The Mathematician

Q: What is infinity? (A brief introduction to infinite sets, infinite limits, and infinite numbers)

Mathematician: To mathematicians, infinity is not a single entity, but rather a label given to a variety of related mathematical objects. What unites these “infinities” is that they are all, in some sense, larger than anything that can be obtained … Continue reading

Posted in -- By the Mathematician, Math, Philosophical | 9 Comments

Q: Is it possible to choose an item from an infinite set of items such that each one has an equal chance of being selected?

The complete question was: The other day I was trying to explain the difference between “impossible” and “with probability zero” to a friend. I remarked “if you pick an integer, and I pick an integer, the mathematical probability that we … Continue reading

Posted in -- By the Mathematician, Math, Probability | 18 Comments

Q: Why is the number 1 not considered a prime number?

Mathematician: Note that when we say that a number is “prime”, all that we are doing is applying a definition that was devised by mathematicians. A prime number is generally defined to be any positive number that has exactly two … Continue reading

Posted in -- By the Mathematician, Math, Number Theory | 41 Comments

Q: If two trains move towards each other at certain velocities, and a fly flies between them at a certain constant speed, how much distance will the fly cover before they crash?

The brain teaser comes in a many variations. For example: Trains A and B, 700 miles apart, are heading toward each other on a straight piece of track. Train A is going 85 mph while train B is going 55 … Continue reading

Posted in -- By the Mathematician, Brain Teaser, Math | 13 Comments

Q: What are the Intersecting Chord and Power of a Point Theorems?

Mathematician: The Intersecting Chords theorem asks us to consider two intersecting line segments inside of a circle (such that each line segment starts and ends on the edge of the circle). Each line segment can be thought of as being … Continue reading

Posted in -- By the Mathematician, Geometry, Math | Leave a comment

Q: Why does the leading digit 1 appear more often than other digits in all sorts of numbers? What’s the deal with Benford’s Law?

Mathematician: Benford’s Law (sometimes called the Significant-Digit Law) states that when we gather numbers from many different types of random sources (e.g. the front pages of newspapers, tables of physical constants at the back of science textbooks, the heights of … Continue reading

Posted in -- By the Mathematician, Math | 1 Comment