Integers_and_Absolute_Value
... • Because AV is a distance, it is always positive. – There is no such thing as a negative distance. – If I drive 11 miles to school, I drive 11 miles home, not -11 miles! ...
... • Because AV is a distance, it is always positive. – There is no such thing as a negative distance. – If I drive 11 miles to school, I drive 11 miles home, not -11 miles! ...
Lecture 2: Section 1.2: Exponents and Radicals Positive Integer
... The proofs of these rules are not very difficult and can be found in the textbook. For example to prove the first law when m and n are positive integers, we see that am an = |a · a · a{z· · · · · a} |a · a · a ·{za · · · · · a} = |a · a · a · a ·{za · a · · · · · a} = am+n n factors m factors m + n ...
... The proofs of these rules are not very difficult and can be found in the textbook. For example to prove the first law when m and n are positive integers, we see that am an = |a · a · a{z· · · · · a} |a · a · a ·{za · · · · · a} = |a · a · a · a ·{za · a · · · · · a} = am+n n factors m factors m + n ...
attached worksheet
... decimal point is 10 (that is 17 goes into 1.0 zero times with a remainder of 10); that 17 goes into 100 five times with a remainder of 15 (Look where the 5 and 15 appear on the circle in Figure 2.); that 17 goes into 150 eight times with remainder 14. Furthermore, check that 15/17 begins .88235... . ...
... decimal point is 10 (that is 17 goes into 1.0 zero times with a remainder of 10); that 17 goes into 100 five times with a remainder of 15 (Look where the 5 and 15 appear on the circle in Figure 2.); that 17 goes into 150 eight times with remainder 14. Furthermore, check that 15/17 begins .88235... . ...
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.