Introduction to Real Analysis
... (d) If p>1 and α is real, then lim n p (e) If |p| < 1, then lim p n 0 lim ...
... (d) If p>1 and α is real, then lim n p (e) If |p| < 1, then lim p n 0 lim ...
ch42 - Kent State University
... • The proof of the undecidability of the halting problem uses a technique called diagonalization, discovered first by mathematician Georg Cantor in 1873. • Cantor was concerned with the problem of measuring the sizes of infinite sets. If we have two infinite sets, how can we tell whether one is larg ...
... • The proof of the undecidability of the halting problem uses a technique called diagonalization, discovered first by mathematician Georg Cantor in 1873. • Cantor was concerned with the problem of measuring the sizes of infinite sets. If we have two infinite sets, how can we tell whether one is larg ...
Maths Investigation Ideas for A-level, IB and Gifted
... 8) Squaring the circle: This is a puzzle from ancient times - which was to find out whether a square could be created that had the same area as a given circle. It is now used as a saying to represent something impossible. 9) Polyominoes: These are shapes made from squares. The challenge is to see ho ...
... 8) Squaring the circle: This is a puzzle from ancient times - which was to find out whether a square could be created that had the same area as a given circle. It is now used as a saying to represent something impossible. 9) Polyominoes: These are shapes made from squares. The challenge is to see ho ...
Operaciones con números racionales
... Find the decimal expression of the following fractions. You can use the calculator, but may be, in some cases, you will need to divide by yourself ! ...
... Find the decimal expression of the following fractions. You can use the calculator, but may be, in some cases, you will need to divide by yourself ! ...
Terminology of Algebra
... • It may seem that rational numbers would fill up all the gaps between integers on a number line, but they don’t • The next set of numbers to be considered will fill in the rest of the gaps between the integers and rational numbers on a number line • Irrational numbers – Numbers that can not be writ ...
... • It may seem that rational numbers would fill up all the gaps between integers on a number line, but they don’t • The next set of numbers to be considered will fill in the rest of the gaps between the integers and rational numbers on a number line • Irrational numbers – Numbers that can not be writ ...
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.