Infinity is a mathematical concept originating from Zeno of Elia (~450 BC) who tried to show its “physical” impossibility. This resulted in the “arrow paradox”, but which was solved later on. Many mathematicians and physicists went on to try understanding infinity and to explain it by various theories and experiments.
The ancient Greeks expressed infinity by the word apeiron, which had connotations of being unbounded, indefinite, undefined, and formless. One of the earliest appearances of infinity in mathematics regards the ratio between the diagonal and the side of a square. Pythagoras (c.
Son of Danish parents, the mathematician Georg Cantor is one of the creators of the International Congress of Mathematicians (ICM) alongside with Felix Klein. Born in Russia in 1845, he emigrated as a child with his family to Germany.
“An equation means nothing to me unless it expresses a thought of God”, words of the greatest mathematician of our motherland and a great devotee of goddess Kali. Srinivasa Ramanujan, the man who turned equations as his own language and sewed theorems with strings of numbers in his mind.
Infinite series for pi: In 1914, Ramanujan found a formula for infinite series for pi, which forms the basis of many algorithms used today. Finding an accurate approximation of π (pi) has been one of the most important challenges in the history of mathematics.
For those of you who are unfamiliar with this series, which has come to be known as the Ramanujan Summation after a famous Indian mathematician named Srinivasa Ramanujan, it states that if you add all the natural numbers, that is 1, 2, 3, 4, and so on, all the way to infinity, you will find that it is equal to -1/12.
The fundamental principle of the philosophy of Benedict de Spinoza is the necessary and absolute infinity of God. He defined God as an absolutely infinite being. This concept is the starting point of his philosophy.
Aristotle handled the topic of infinity in Physics and in Metaphysics. He distinguished between actual and potential infinity. Actual infinity is completed and definite, and consists of infinitely many elements. Potential infinity is never complete: elements can be always added, but never infinitely many.
Infinity is not a number. Instead, it's a kind of number. You need infinite numbers to talk about and compare amounts that are unending, but some unending amounts—some infinities—are literally bigger than others.
Therefore it is said that Aryabhatta found zero.
The symbol ∞ which we use for infinity today, was first used by John Wallis who used it in De sectionibus conicis Ⓣ in 1655 and again in Arithmetica infinitorum Ⓣ in 1656. He chose it to represent the fact that one could traverse the curve infinitely often.
1. Pythagoras. The life of the famous Greek Pythagoras is somewhat mysterious. Probably born the son of a seal engraver on the island of Samos, Pythagoras has been attributed with many scientific and mathematical discoveries in antiquity.
Value of Infinity
Infinity is not a real number; it has no value.
The first calculation of π was done by Archimedes of Syracuse (287–212 BC), one of the greatest mathematicians of the ancient world.
Beyond the infinity known as ℵ0 (the cardinality of the natural numbers) there is ℵ1 (which is larger) … ℵ2 (which is larger still) … and, in fact, an infinite variety of different infinities.
As no number is imagined beyond it(no real number is larger than infinity). The symbol (∞) sets the limit or unboundedness in calculus.
In modern mysticism, the infinity symbol has become identified with a variation of the ouroboros, an ancient image of a snake eating its own tail that has also come to symbolize the infinite, and the ouroboros is sometimes drawn in figure-eight form to reflect this identification—rather than in its more traditional ...
'' 1 Elsewhere the Bible says of God, ``Behold, the heaven and heaven of heavens cannot contain thee. '' 2 To be infinite is to be without limits. Where there's a limit there's finiteness. Being truly infinite, God knows no restrictions of space, ability, or power.
Christian Tradition.
While some Greek philosophical schools, such as the Stoics, conceived matter to be infinite, Christian theologians consistently attributed infinity to God in the absolute sense.
There is no number before infinity. It is possible to represent infinity minus one as a mathematical expression, but it does not actually equal anything or have any real mathematical value.
Multiplication Property
If a number is multiplied by infinity, then the value of the product is also equal to infinity.
If you add one to infinity, you still have infinity; you don't have a bigger number. If you believe that, then infinity is not a number.
Given series: 1 - 1/3 + 1/9 - 1/27 + ... This is a geometric progression with first term (a) = 1 and common ratio (r) = -1/3. Therefore, the sum of the infinite G.P. is 0.75, which is option (c).
Srinivasa Ramanujan, the brilliant twentieth century Indian mathematician, has been compared with all-time greats like Euler, Gauss and Jacobi, for his natural mathematical genius.