1-Integers - Laurel County Schools
... You can compare and order integers by graphing them on a number line. Integers increase in value as you move to the right along a number line. They decrease in value as you move to the ...
... You can compare and order integers by graphing them on a number line. Integers increase in value as you move to the right along a number line. They decrease in value as you move to the ...
MATH 115, SUMMER 2012 LECTURE 5 Last time:
... - defined congruence - listed a bunch of properties, similar to “=”, except that we can’t always “cancel” - defined complete residue system mod m - one representative per residue class - forgot to mention: if a ≡ b mod m, then (a, m) = (b, m). 1. Reduced Residue Systems and the φ-function Since we c ...
... - defined congruence - listed a bunch of properties, similar to “=”, except that we can’t always “cancel” - defined complete residue system mod m - one representative per residue class - forgot to mention: if a ≡ b mod m, then (a, m) = (b, m). 1. Reduced Residue Systems and the φ-function Since we c ...
3.2
... How to tell if one fraction is bigger than another A. See if the fractions have the same denominator B. If not, scale them up to the LCM of the denominators (find the common denominator) C. Compare the numerators to see which is bigger Ex1: 5/12 and 7/18 A. Denominators not the same B. LCM of 12 & 1 ...
... How to tell if one fraction is bigger than another A. See if the fractions have the same denominator B. If not, scale them up to the LCM of the denominators (find the common denominator) C. Compare the numerators to see which is bigger Ex1: 5/12 and 7/18 A. Denominators not the same B. LCM of 12 & 1 ...
![[Chap. 2] Pythagorean Triples (b) The table suggests that in every](http://s1.studyres.com/store/data/016288292_1-0734630555f52d6c6864c2800221c690-300x300.png)
[Chap. 2] Pythagorean Triples (b) The table suggests that in every
... This gives a primitive Pythagorean triple with the right value of b provided that B > 2r−1 . On the other hand, if B < 2r−1 , then we can just take a = 22r−2 − B 2 instead. (c) This part is quite difficult to prove, and it’s not even that easy to make the correct conjecture. It turns out that an odd ...
... This gives a primitive Pythagorean triple with the right value of b provided that B > 2r−1 . On the other hand, if B < 2r−1 , then we can just take a = 22r−2 − B 2 instead. (c) This part is quite difficult to prove, and it’s not even that easy to make the correct conjecture. It turns out that an odd ...
Collatz conjecture
The Collatz conjecture is a conjecture in mathematics named after Lothar Collatz, who first proposed it in 1937. The conjecture is also known as the 3n + 1 conjecture, the Ulam conjecture (after Stanisław Ulam), Kakutani's problem (after Shizuo Kakutani), the Thwaites conjecture (after Sir Bryan Thwaites), Hasse's algorithm (after Helmut Hasse), or the Syracuse problem; the sequence of numbers involved is referred to as the hailstone sequence or hailstone numbers (because the values are usually subject to multiple descents and ascents like hailstones in a cloud), or as wondrous numbers.Take any natural number n. If n is even, divide it by 2 to get n / 2. If n is odd, multiply it by 3 and add 1 to obtain 3n + 1. Repeat the process (which has been called ""Half Or Triple Plus One"", or HOTPO) indefinitely. The conjecture is that no matter what number you start with, you will always eventually reach 1. The property has also been called oneness.Paul Erdős said about the Collatz conjecture: ""Mathematics may not be ready for such problems."" He also offered $500 for its solution.