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[Part 2]
... £2(1,3) = 120. A really significant result would be a proof that this is true for a and b any two successive Fibonacci numbers of even index. To show this independently from their result would present all the difficulties they encountered for their special case. At one time I hoped that one might by ...
... £2(1,3) = 120. A really significant result would be a proof that this is true for a and b any two successive Fibonacci numbers of even index. To show this independently from their result would present all the difficulties they encountered for their special case. At one time I hoped that one might by ...
Algebra 1 - Teacher Pages
... Rational numbers are numbers that can be expressed in the form a/b, where a and b are both integers and b ≠ 0. When expressed as a decimal, a rational number is either a terminating decimal or a repeating decimal. A terminating decimal has an end. A repeating decimal has a block of one or more digi ...
... Rational numbers are numbers that can be expressed in the form a/b, where a and b are both integers and b ≠ 0. When expressed as a decimal, a rational number is either a terminating decimal or a repeating decimal. A terminating decimal has an end. A repeating decimal has a block of one or more digi ...
PERSPEX MACHINE IX: TRANSREAL ANALYSIS COPYRIGHT
... We introduce transreal analysis as a generalisation of real analysis. We find that the generalisation of the real exponential and logarithmic functions is well defined for all transreal numbers. Hence, we derive well defined values of all transreal powers of all non-negative transreal numbers. In pa ...
... We introduce transreal analysis as a generalisation of real analysis. We find that the generalisation of the real exponential and logarithmic functions is well defined for all transreal numbers. Hence, we derive well defined values of all transreal powers of all non-negative transreal numbers. In pa ...
Situation 46: Division Involving Zero
... For situations involving division with zero, there are three types of forms: 0, undefinable, and indeterminate. The indeterminate form has particular importance in a calculus setting in that: given a function, f, that would be continuous everywhere except that f(a) is indeterminate, we can select a ...
... For situations involving division with zero, there are three types of forms: 0, undefinable, and indeterminate. The indeterminate form has particular importance in a calculus setting in that: given a function, f, that would be continuous everywhere except that f(a) is indeterminate, we can select a ...
QUIZ/MIDTERM #1 SOLUTIONS (1) For each of the following
... is closed. For a slightly less trivial answer, let X be any closed set, and then take the collection consisting of single point sets {x}, where x ranges over points in X. Then the union of these sets is X, which is closed. (b) In line with the previous solution, perhaps the simplest solution is to l ...
... is closed. For a slightly less trivial answer, let X be any closed set, and then take the collection consisting of single point sets {x}, where x ranges over points in X. Then the union of these sets is X, which is closed. (b) In line with the previous solution, perhaps the simplest solution is to l ...
Chapter 1
... (or ratio of two integers), i.e. rational numbers = { q , where p and q are integers and q 0}. E.g 2/3, 9/2, 5/1. Note that all integers n are rational numbers, since n = n/1. Is 4/ a rational number? A rational number written as a fraction can be written in a decimal notation by dividing the nu ...
... (or ratio of two integers), i.e. rational numbers = { q , where p and q are integers and q 0}. E.g 2/3, 9/2, 5/1. Note that all integers n are rational numbers, since n = n/1. Is 4/ a rational number? A rational number written as a fraction can be written in a decimal notation by dividing the nu ...
Irrational Numbers
... Irrational numbers are decimals that never end, but they don’t repeat either. This means they cannot be written as fractions. All fractions convert to decimals that either end or repeat. (Decimals that end actually have a repeating pattern of zeros.) ...
... Irrational numbers are decimals that never end, but they don’t repeat either. This means they cannot be written as fractions. All fractions convert to decimals that either end or repeat. (Decimals that end actually have a repeating pattern of zeros.) ...
Infinity
Infinity (symbol: ∞) is an abstract concept describing something without any limit and is relevant in a number of fields, predominantly mathematics and physics.In mathematics, ""infinity"" is often treated as if it were a number (i.e., it counts or measures things: ""an infinite number of terms"") but it is not the same sort of number as natural or real numbers. In number systems incorporating infinitesimals, the reciprocal of an infinitesimal is an infinite number, i.e., a number greater than any real number; see 1/∞.Georg Cantor formalized many ideas related to infinity and infinite sets during the late 19th and early 20th centuries. In the theory he developed, there are infinite sets of different sizes (called cardinalities). For example, the set of integers is countably infinite, while the infinite set of real numbers is uncountable.