100 Statements to Prove for CS 2233 The idea of this
... 1. For each of the following statements, either prove it or show a counterexample: If R is reflexive, then R ∘ R is also reflexive. If R is symmetric, then R ∘ R is also symmetric. If R is antisymmetric, then R ∘ R is also antisymmetric. If R is transitive, then R ∘ R is also transitive. 2. For each ...
... 1. For each of the following statements, either prove it or show a counterexample: If R is reflexive, then R ∘ R is also reflexive. If R is symmetric, then R ∘ R is also symmetric. If R is antisymmetric, then R ∘ R is also antisymmetric. If R is transitive, then R ∘ R is also transitive. 2. For each ...
Learning Strategies PDF
... Grade 5 Number SO7: Demonstrate an understanding of fractions by using concrete, pictorial and symbolic representations to: create sets of equivalent fractions compare fractions with like and unlike denominators. Grade 6 Number SO4: Relate improper fractions to mixed numbers and mixed numbers to imp ...
... Grade 5 Number SO7: Demonstrate an understanding of fractions by using concrete, pictorial and symbolic representations to: create sets of equivalent fractions compare fractions with like and unlike denominators. Grade 6 Number SO4: Relate improper fractions to mixed numbers and mixed numbers to imp ...
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.