Sequences - UNM Computer Science
... an−1 + 1 for n ≥ 2 and a1 = 1. In this definition, the term a1 is the exit (or initial) condition of the recursive function. Without it, the sequence is not well-defined. Example 10 The mathematical sequence defined recursively as: an = an−1 + 1 for n ≥ 2 and a1 = 10 is also arithmetic. We can itera ...
... an−1 + 1 for n ≥ 2 and a1 = 1. In this definition, the term a1 is the exit (or initial) condition of the recursive function. Without it, the sequence is not well-defined. Example 10 The mathematical sequence defined recursively as: an = an−1 + 1 for n ≥ 2 and a1 = 10 is also arithmetic. We can itera ...
Notes on complex numbers
... well about the natural numbers is that they count whole numbers of objects, and that we can talk about adding and multiplying two natural numbers. What doesn’t work well is that we can’t always talk about subtracting two natural numbers, e.g. there is no natural number which is equal to 3 − 7. Resta ...
... well about the natural numbers is that they count whole numbers of objects, and that we can talk about adding and multiplying two natural numbers. What doesn’t work well is that we can’t always talk about subtracting two natural numbers, e.g. there is no natural number which is equal to 3 − 7. Resta ...
Leftist Numbers
... begin, it will be helpful to look at the multiplicative inverses of leftist numbers. If we are able to find the multiplicative inverses of all naturals, then we are well on our way to proving that all rationals exist since we will have all possible denominators represented. Now, in order to prove th ...
... begin, it will be helpful to look at the multiplicative inverses of leftist numbers. If we are able to find the multiplicative inverses of all naturals, then we are well on our way to proving that all rationals exist since we will have all possible denominators represented. Now, in order to prove th ...
Section 2.3: Infinite sets and cardinality
... Suppose that A and B are sets (finite or infinite). We say that A and B have the same cardinality (written |A| = |B|) if a bijective correspondence exists between A and B. In other words, A and B have the same cardinality if it’s possible to match each element of A to a different element of B in such a ...
... Suppose that A and B are sets (finite or infinite). We say that A and B have the same cardinality (written |A| = |B|) if a bijective correspondence exists between A and B. In other words, A and B have the same cardinality if it’s possible to match each element of A to a different element of B in such a ...
Module 1 Structure o..
... numbers since both sets have names that start with the same letter. The joke about P is that only someone who is psychic can understand them. On an additional note the prefix “ir” means beside. So the irrational numbers are beside the rational numbers in the number line. And they are! Just to the le ...
... numbers since both sets have names that start with the same letter. The joke about P is that only someone who is psychic can understand them. On an additional note the prefix “ir” means beside. So the irrational numbers are beside the rational numbers in the number line. And they are! Just to the le ...
Chapter 4 – Formulas and Negative Numbers Section 4A
... subtract negative numbers? That is the topic of this section. The key to subtracting signed numbers is the idea of an opposite. Opposites have the same number, but have the opposite sign. For example the opposite of -4 is +4. The opposite of +7.241 is -7.241. Look at the following key example. Suppo ...
... subtract negative numbers? That is the topic of this section. The key to subtracting signed numbers is the idea of an opposite. Opposites have the same number, but have the opposite sign. For example the opposite of -4 is +4. The opposite of +7.241 is -7.241. Look at the following key example. Suppo ...
