Fraction Terms - Del Mar College
... Fraction: The numbers used to express the ratio of two numbers and are used primarily to express a comparison between the parts and the whole. The following are some fractions: 3/4, 5/6 and 7/10. Proper fraction: A fraction in which the numerator is less than the denominator. The fractions 5/6 and 1 ...
... Fraction: The numbers used to express the ratio of two numbers and are used primarily to express a comparison between the parts and the whole. The following are some fractions: 3/4, 5/6 and 7/10. Proper fraction: A fraction in which the numerator is less than the denominator. The fractions 5/6 and 1 ...
Properties of numbers 1.1 - Pearson Schools and FE Colleges
... What do you notice about the last digit of multiples of ten? Establish that they all end in zero. Repeat the starter activity with multiples of 10, saying three consecutive multiples of 10, and asking pupils to say the next three. Try counting forwards and counting backwards. Say that counting on or ...
... What do you notice about the last digit of multiples of ten? Establish that they all end in zero. Repeat the starter activity with multiples of 10, saying three consecutive multiples of 10, and asking pupils to say the next three. Try counting forwards and counting backwards. Say that counting on or ...
Exceptional real Lucas sequences
... (L, j|f) = 1 implies (P4P5, P6) = 1 by Theorem 2.1 of [3], and P6 is even if and only if P 3 is. Thus for p an odd prime, p | P6 but p \ P^JPJP^ if and only if p \ Q6. On the other hand, if p \ L, then p\ P2p by Theorem 2.0 of [3], so p I (Q6, L) if and only if L is odd and p = 3. Now Q6 = 2*3W, I = ...
... (L, j|f) = 1 implies (P4P5, P6) = 1 by Theorem 2.1 of [3], and P6 is even if and only if P 3 is. Thus for p an odd prime, p | P6 but p \ P^JPJP^ if and only if p \ Q6. On the other hand, if p \ L, then p\ P2p by Theorem 2.0 of [3], so p I (Q6, L) if and only if L is odd and p = 3. Now Q6 = 2*3W, I = ...
Document
... that in the Pascal triangle when the entries are taken mod 2, certain triangles drawn repeat themselves (see figure below). (The repeating pattern of triangles is known as Serpinski's casket.) To prove this we need: ...
... that in the Pascal triangle when the entries are taken mod 2, certain triangles drawn repeat themselves (see figure below). (The repeating pattern of triangles is known as Serpinski's casket.) To prove this we need: ...
Full text
... To this end, working from left to right, we insert the coefficients (αβ)0 , (αβ)2k , (αβ)4k , and (αβ)6k . In summary, (2.13) is an equation that is homogeneous of degree 6 in n, and homogeneous of degree 12 in k. To complete the proof, it suffices to verify that (2.13) is true for seven distinct va ...
... To this end, working from left to right, we insert the coefficients (αβ)0 , (αβ)2k , (αβ)4k , and (αβ)6k . In summary, (2.13) is an equation that is homogeneous of degree 6 in n, and homogeneous of degree 12 in k. To complete the proof, it suffices to verify that (2.13) is true for seven distinct va ...
12-1 Define and Use Sequences and Series
... * A sequence is a function whose domain is a set of consecutive integers. If the domain is not specified, it starts with 1. The values of the range are called the terms of the sequence. Domain: 1 2 3 4 … n Range: a1 a2 a3 a4 … an ...
... * A sequence is a function whose domain is a set of consecutive integers. If the domain is not specified, it starts with 1. The values of the range are called the terms of the sequence. Domain: 1 2 3 4 … n Range: a1 a2 a3 a4 … an ...
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.