- What is the value of infinity?
- Are infinities equal?
- What Is Set Theory?
- Can you compare infinities?
- Are all countable infinities equal?
- Why all infinities are equal?
- Who invented algebra?
- Who is the father of set?
The initial value of Infinity is Number.
Two mathematicians have proved that two different infinities are equal in size, settling a long-standing question. Their proof rests on a surprising link between the sizes of infinities and the complexity of mathematical theories.
Set theory is the mathematical theory of well-determined collections, called sets, of objects that are called members, or elements, of the set. The axioms of set theory imply the existence of a set-theoretic universe so rich that all mathematical objects can be construed as sets.
After he established that the sizes of infinite sets can be compared by putting them into one-to-one correspondence with each other, Cantor made an even bigger leap: He proved that some infinite sets are even larger than the set of natural numbers. Thus, a second kind of infinity was born: the uncountably infinite.
(b) No, all countable infinities are the same: if A and B are both countable and infinite, then α=β.
Therefore, while both ranges have an infinite number of numbers, there must be the same number of numbers in both ranges, because we have a 1:1 transformation possible between the two sets, by which every number in one set can be converted to a number in the other set and vice-versa, with no overlap (no two values from
Muhammad ibn Musa al-KhwarizmiMuhammad ibn Musa al-Khwarizmi was a 9th-century Muslim mathematician and astronomer. He is known as the “father of algebra”, a word derived from the title of his book, Kitab al-Jabr. His pioneering work offered practical answers for land distribution, rules on inheritance and distributing salaries.
Georg Ferdinand Ludwig Philipp CantorGeorg Cantor, in full Georg Ferdinand Ludwig Philipp Cantor, (born March 3, 1845, St. Petersburg, Russia—died January 6, 1918, Halle, Germany), German mathematician who founded set theory and introduced the mathematically meaningful concept of transfinite numbers, indefinitely large but distinct from one another.