Alexander Humez - Collected Quotes

"A sequence can be finite or infinite. One way of defining a finite sequence is to list every one of its terms. But to define an infinite sequence, the terms must be capable of being generated, in order, by some procedure with a predictable result for each place in the string." (Alexander Humez et al, "Zero to Lazy Eight: The romance of numbers", 1993)

"An infinite set is any set from which you can remove some members without reducing its size. In fact, we can start with an infinite set, remove an infinite set, and still have an infinite set left behind […]." (Alexander Humez et al, "Zero to Lazy Eight: The romance of numbers", 1993)

"Finite-state machines, fundamental to the automatic translation and interpretation of languages used by computer programmers, can accept a limited set of inputs, and as the name implies, allow only a limited number of states. […] When it receives an input item (a coin for the vending machine, a pitch for the baseball count), the finite-state machine chooses a subsequent state based on both the input and the current state." (Alexander Humez et al, "Zero to Lazy Eight: The romance of numbers", 1993)

"In mathematics, a function is a sort of converter: It converts a value to some other value. […] the mathematical definition of a continuous function requires that any small change in the input will result in a small change to the output." (Alexander Humez et al, "Zero to Lazy Eight: The romance of numbers", 1993)

"Like the noble gases (helium, neon, argon, krypton, xenon, and radon), primes exist in splendid isolation; conversely, any composite number is the product of a unique set of prime factors." (Alexander Humez et al, "Zero to Lazy Eight: The romance of numbers", 1993)

"'Randomness', too, is in the eye of the beholder." (Alexander Humez et al, "Zero to Lazy Eight: The romance of numbers", 1993)

"The four-color map theorem is an assertion about graph theory, which is the study of discrete points and the lines that connect them; each point is called a vertex and each line is called an edge." (Alexander Humez et al, "Zero to Lazy Eight: The romance of numbers", 1993)

"Why is it so important to find primes, or to show that a certain integer is one? A very practical application in cryptography rests on the fact that since it is extremely hard to factor very large numbers, a two-hundred-digit number that was the product of two primes could govern text encoding: It would be virtually impossible to guess what the two numbers were if you didn't know them in advance, and out of the question (save perhaps on a state-of-the-art supercomputer) to go at it by trial and error." (Alexander Humez et al, "Zero to Lazy Eight: The romance of numbers", 1993)

"Zero is the only number that is neither positive nor negative. As such, it represents a quantity: If three is the name we give to the number of items in a trilogy, a trinity, or a triad, zero is our name for the number of items in an empty, or null set, i.e., one having no members. This is not the same as saying the set doesn't exist; in fact, we can and do make valid assertions about null sets […]" (Alexander Humez et al, "Zero to Lazy Eight: The romance of numbers", 1993)

"Zero is where it all begins, the clean slate. We speak of zero-sum games (in which anyone who wins anything does so only at the equal expense of the losers), zero hour (the time at which a military operation begins), ground zero (the impact point of a bomb, particularly a nuclear one), to zero in on something (getting it precisely in the cross hairs), zero degrees of temperature-which, depending on the scale you use, can be the freezing point of water (Centigrade), fortified wine (Fahrenheit), or the universe (Kelvin); the last, a bit chillier than - 2730 C or - 459' F, is aptly called absolute zero." (Alexander Humez et al, "Zero to Lazy Eight: The romance of numbers", 1993)