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{\displaystyle x=\infty } on the projectively extended real line. Division by zero Extended complex plane Extended natural numbers Improper integral Infinity Log semiring...

projectively extended real line extends the field of real numbers in the same way that the Riemann sphere extends the field of complex numbers, by adding...

real, used in the 17th century by René Descartes, distinguishes real numbers from imaginary numbers such as the square roots of −1. The real numbers include...

real numbers such as the square root of 2 ( 2 ) {\displaystyle \left({\sqrt {2}}\right)} and π, and complex numbers which extend the real numbers with...

mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted i, called the imaginary unit and...

When considered as a subset of the extended reals formed by adding two "numbers" or "points" to the real numbers (namely negative infinity, denoted −...

\mathbb {N} ^{\infty }} . It is a subset of the extended real number line, which extends the real numbers by adding − ∞ {\displaystyle -\infty } and + ∞...

mathematics, a (real) interval is the set of all real numbers lying between two fixed endpoints with no "gaps". Each endpoint is either a real number or positive...

In mathematics, there are several equivalent ways of defining the real numbers. One of them is that they form a complete ordered field that does not contain...

numbers (also known as real transcendental numbers or transcendental irrational numbers) are irrational numbers, since all rational numbers are algebraic. The...

1}(x+1)=2.} The affinely extended real numbers are obtained from the real numbers R {\displaystyle \mathbb {R} } by adding two new numbers + ∞ {\displaystyle...

positive real numbers inside the positive real numbers (as their own superset), nor any infimum of the positive real numbers inside the complex numbers with...

include the set of natural numbers, extended real numbers, transfinite numbers, or even an infinite sequence of rational numbers. Actual infinity is to be...

of real analysis studies the behavior of real numbers, sequences and series of real numbers, and real functions. Some particular properties of real-valued...

a real closed field is a field F that has the same first-order properties as the field of real numbers. Some examples are the field of real numbers, the...

mathematics, hyperreal numbers are an extension of the real numbers to include certain classes of infinite and infinitesimal numbers. A hyperreal number...

Q . {\displaystyle \mathbb {Q} .} ⁠ A rational number is a real number. The real numbers that are rational are those whose decimal expansion either terminates...

Y=[-\infty ,\infty ]=\mathbb {R} \cup \{\pm \infty \}} are the extended real numbers. In this case, if f {\displaystyle f} is identically equal to ∞...

called nonnegative homogeneity. However, for functions valued in the extended real numbers [ − ∞ , ∞ ] = R ∪ { ± ∞ } , {\displaystyle [-\infty ,\infty ]=\mathbb...

In idempotent analysis, the tropical semiring is a semiring of extended real numbers with the operations of minimum (or maximum) and addition replacing...