Chapter 1
... 6.1.1.3. Using two integers to describe part of a whole 6.1.1.3.1. Need more language to describe part-whole relationship 6.1.1.3.2. number of pieces of interest vs. number of pieces found in the original whole ...
... 6.1.1.3. Using two integers to describe part of a whole 6.1.1.3.1. Need more language to describe part-whole relationship 6.1.1.3.2. number of pieces of interest vs. number of pieces found in the original whole ...
Carryless Arithmetic Mod 10
... so one of f 2 , f 5 must be irreducible and the other must be a unit. So the irreducible elements in R10 [X ] are of the form [ f 2 (X ), u], where f 2 (X ) is an irreducible polynomial mod 2 of degree ≥ 1 and u ∈ {1, 2, 3, 4}, together with elements of the form [1, f 5 (X )], where f 5 (X ) is an i ...
... so one of f 2 , f 5 must be irreducible and the other must be a unit. So the irreducible elements in R10 [X ] are of the form [ f 2 (X ), u], where f 2 (X ) is an irreducible polynomial mod 2 of degree ≥ 1 and u ∈ {1, 2, 3, 4}, together with elements of the form [1, f 5 (X )], where f 5 (X ) is an i ...
AMATYC Contest (Fall 2008) Solutions
... 5th rows; the same argument is repeated one more round, then it’s clear it won’t work. 16 1x3s would work: Fill the 3-cell col with a single 1x3, with the rest covered by horizontal 1x3s. Now prove that 24 1x2s won’t work: Suppose it did. Among all such coverings there would be one minimizing the nu ...
... 5th rows; the same argument is repeated one more round, then it’s clear it won’t work. 16 1x3s would work: Fill the 3-cell col with a single 1x3, with the rest covered by horizontal 1x3s. Now prove that 24 1x2s won’t work: Suppose it did. Among all such coverings there would be one minimizing the nu ...
adding-subtracting-real-numbers-1-2
... What if…? The tallest known iceberg in the North Atlantic rose 550 feet above the oceans surface. How many feet would it be from the top of the tallest iceberg to the wreckage of the Titanic, which is at an elevation of –12,468 feet? ...
... What if…? The tallest known iceberg in the North Atlantic rose 550 feet above the oceans surface. How many feet would it be from the top of the tallest iceberg to the wreckage of the Titanic, which is at an elevation of –12,468 feet? ...
Łukasiewicz`s Logic and Prime Numbers
... of Łukasiewicz's finite-valued logics Ln+1. The approaches of this kind we call external. The only means to penetrate into the essence of logic is to represent it as a functional system. It was exactly this approach that allowed to discover that functional properties of Ln+1 are highly unusual. V.K. ...
... of Łukasiewicz's finite-valued logics Ln+1. The approaches of this kind we call external. The only means to penetrate into the essence of logic is to represent it as a functional system. It was exactly this approach that allowed to discover that functional properties of Ln+1 are highly unusual. V.K. ...
Applications of the Complex Roots of Unity - Rose
... This formula shows that the factoring of Mersenne numbers merely depends on the exponent (n). We are making the assumption that the first time a prime factor appears it will have an exponent of 1, which is the assumption we made earlier. Assuming that expression (6) is true we offer the following pr ...
... This formula shows that the factoring of Mersenne numbers merely depends on the exponent (n). We are making the assumption that the first time a prime factor appears it will have an exponent of 1, which is the assumption we made earlier. Assuming that expression (6) is true we offer the following pr ...
1-2 - Plain Local Schools
... What if…? The tallest known iceberg in the North Atlantic rose 550 feet above the oceans surface. How many feet would it be from the top of the tallest iceberg to the wreckage of the Titanic, which is at an elevation of –12,468 feet? ...
... What if…? The tallest known iceberg in the North Atlantic rose 550 feet above the oceans surface. How many feet would it be from the top of the tallest iceberg to the wreckage of the Titanic, which is at an elevation of –12,468 feet? ...