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A typical problem in this area of mathematics is to work out whether a given number is transcendental. Cantor used a cardinality argument to show that there are only countably many algebraic numbers, and hence almost all numbers are transcendental.
For example, π and (1 − π) are both transcendental, but π + (1 − π) = 1 is obviously not. It is unknown whether e + π, for example, is transcendental, though at least one of e + π and eπ must be transcendental. More generally, for any two transcendental numbers a and b, at least one of a + b and ab must be transcendental.
In the example from "Double rounding" section, rounding 9.46 to one decimal gives 9.4, which rounding to integer in turn gives 9. With binary arithmetic, this rounding is also called "round to odd" (not to be confused with "round half to odd"). For example, when rounding to 1/4 (0.01 in binary), x = 2.0 ⇒ result is 2 (10.00 in binary)
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
Goldbach’s Conjecture. One of the greatest unsolved mysteries in math is also very easy to write. Goldbach’s Conjecture is, “Every even number (greater than two) is the sum of two primes ...
Hilbert's seventh problem is one of David Hilbert's list of open mathematical problems posed in 1900. It concerns the irrationality and transcendence of certain numbers ( Irrationalität und Transzendenz bestimmter Zahlen ).
An open problem in number theory settled by the conjecture is the question of whether there exists a non-integer real number t such that both 2 t and 3 t are integers, or indeed such that a t and b t are both integers for some pair of integers a and b that are multiplicatively independent over the integers.
Pages in category "Unsolved problems in number theory" The following 106 pages are in this category, out of 106 total. This list may not reflect recent changes .