Mathematics Grade 8 - Pompton Lakes School District
... 1.) Compare rational and irrational numbers to demonstrate that the decimal expansion of irrational numbers do not repeat; show that every rational number has a decimal expansion which eventually repeats and covert such decimals into rational numbers. 2.) Use rational numbers to approximate and loca ...
... 1.) Compare rational and irrational numbers to demonstrate that the decimal expansion of irrational numbers do not repeat; show that every rational number has a decimal expansion which eventually repeats and covert such decimals into rational numbers. 2.) Use rational numbers to approximate and loca ...
Factors and Prime Numbers
... The first grid shows all the numbers from 1 to 100. The first prime number is 2, so we keep it, but eliminate, or “sieve out” all the other even numbers, as they all have a factor of 2 as well as 1 and the number itself. Next, we continue in the same vein by getting rid of all the multiples of 3 exc ...
... The first grid shows all the numbers from 1 to 100. The first prime number is 2, so we keep it, but eliminate, or “sieve out” all the other even numbers, as they all have a factor of 2 as well as 1 and the number itself. Next, we continue in the same vein by getting rid of all the multiples of 3 exc ...
REVERSE MATHEMATICS AND RECURSIVE GRAPH THEORY
... Reverse mathematics provides powerful techniques for analyzing the logical content of theorems. By contrast, recursive mathematics analyzes the effective content of theorems. Theorems and techniques of recursive mathematics can often inspire related results in reverse mathematics, as demonstrated by ...
... Reverse mathematics provides powerful techniques for analyzing the logical content of theorems. By contrast, recursive mathematics analyzes the effective content of theorems. Theorems and techniques of recursive mathematics can often inspire related results in reverse mathematics, as demonstrated by ...
lecture1.5
... Disproving something: counterexamples If we are asked to show that a proposition is False, then we just need to provide one counter-example for which the proposition is False In other words, to show that x P(x) is False, we can just show x P(x) = x P(x) to be True Example: “Every positive inte ...
... Disproving something: counterexamples If we are asked to show that a proposition is False, then we just need to provide one counter-example for which the proposition is False In other words, to show that x P(x) is False, we can just show x P(x) = x P(x) to be True Example: “Every positive inte ...
Chapter 2: Introduction to Propositional Logic
... The negation of a true formula is a false formula, and the negation of a false formula is a true formula. This is expressed in the following ...
... The negation of a true formula is a false formula, and the negation of a false formula is a true formula. This is expressed in the following ...
LECTURE 4. RATIONAL AND IRRATIONAL NUMBERS: ORDER
... The first condition means consistency of all equations l 6 x 6 r for all (l, r) ∈ (L, R): its violation would instantly mean that one of the inequalities would have no solutions at all. The second condition means that the common solution to all these inequalities must be unique. Informally it means ...
... The first condition means consistency of all equations l 6 x 6 r for all (l, r) ∈ (L, R): its violation would instantly mean that one of the inequalities would have no solutions at all. The second condition means that the common solution to all these inequalities must be unique. Informally it means ...
