Comparing and Ordering Integers
... A car wash that makes $500 per week. A restaurant that loses $200 per week. A diner that makes $200 per week. A CD store that loses $450 per week. ...
... A car wash that makes $500 per week. A restaurant that loses $200 per week. A diner that makes $200 per week. A CD store that loses $450 per week. ...
![[Part 1]](http://s1.studyres.com/store/data/008795780_1-2d32093eb8955eecb4220b99bc38a981-300x300.png)
Tuesday, August 24
... as a/b, where a and b are both integers, and b is not equal to 0 Irrational Numbers Cannot be expressed in the form a/b where a and b are integers. Note: All integers are rational numbers because you can write any integer as n/1 ...
... as a/b, where a and b are both integers, and b is not equal to 0 Irrational Numbers Cannot be expressed in the form a/b where a and b are integers. Note: All integers are rational numbers because you can write any integer as n/1 ...
Sequences as Functions Learning Task
... The first six sequences above are finite sequences, because they contain a finite number of terms. The last three are infinite sequences because they contain an infinite number of terms. The three dots, called ellipses, indicate that some of the terms are missing. Ellipses are necessary for infinit ...
... The first six sequences above are finite sequences, because they contain a finite number of terms. The last three are infinite sequences because they contain an infinite number of terms. The three dots, called ellipses, indicate that some of the terms are missing. Ellipses are necessary for infinit ...
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.