“There is no doubt that we cannot do without variable quantities in the sense of the potential infinite. But from this very fact the necessity of the actual infinite can be demonstrated.”

— Georg Cantor

"Über die verschiedenen Ansichten in Bezug auf die actualunendlichen Zahlen" ["Over the different views with regard to the actual infinite numbers"] - Bihand Till Koniglen Svenska Vetenskaps Akademiens Handigar (1886)

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Georg Cantor 27

mathematician, inventor of set theory 1845–1918

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“In order for there to be a variable quantity in some mathematical study, the domain of its variability must strictly speaking be known beforehand through a definition. However, this domain cannot itself be something variable, since otherwise each fixed support for the study would collapse. Thus this domain is a definite, actually infinite set of values. Hence each potential infinite, if it is rigorously applicable mathematically, presupposes an actual infinite.”

Georg Cantor (1845–1918) mathematician, inventor of set theory

“It is only by intuition that the infinite can be apprehended. But why is this? Why cannot the infinite be apprehended by concepts? To see this we must understand that the word "infinite," in the religious sense, has nothing at all to do with that sense of the word in which it is applied to space, time, and the number series. We may call this latter the mathematical infinite to distinguish it from the religious infinite. And it is the confusion between these two which misled us into the false trail of supposing that the infinity of God's mind refers to the amount of His knowledge and that the finitude of man's mind refers to his ignorance. The religious infinite, or in other words the infinity of God, means that than 'which there is no other. In this sense neither space nor time could be infinite, since space is an "other" to time, and time is an "other" to space.”

Walter Terence Stace (1886–1967) British civil servant, educator and philosopher.

p. 46-47.

“The potential infinite means nothing other than an undetermined, variable quantity, always remaining finite, which has to assume values that either become smaller than any finite limit no matter how small, or greater than any finite limit no matter how great.”

Georg Cantor (1845–1918) mathematician, inventor of set theory

"Mitteilungen" (1887-8)

“To those who ask what the infinitely small quantity in mathematics is, we answer that it is actually zero. Hence there are not so many mysteries hidden in this concept as they are usually believed to be.”

Leonhard Euler (1707–1783) Swiss mathematician

As quoted in Fundamentals of Teaching Mathematics at University Level (2000) by Benjamin Baumslag, p. 214

“God in His infinite grandeur without any quantity and absolutely indivisible, which we call immensity, is necessarily all in every extension or space or place which exists or can be imagined.”

Nicole Oresme (1323–1382) French philosopher

Book II, Ch. 2, p. 279.
Le livre du ciel et du monde (1377)

“We are a little piece of continual change, looking at an infinite quantity of continual change.”

B.K.S. Iyengar (1918–2014) Indian yoga teacher and scholar

Source: Light on Life: The Yoga Journey to Wholeness, Inner Peace, and Ultimate Freedom, p. 7

“Every quantity is intellectually conceivable as infinitely divisible.”

Leonardo Da Vinci (1452–1519) Italian Renaissance polymath

The Notebooks of Leonardo da Vinci (1883), XIX Philosophical Maxims. Morals. Polemics and Speculations.

“Education alone can conduct us to that enjoyment which is, at once, best in quality and infinite in quantity.”

Horace Mann (1796–1859) American politician

Lecture 1
Lectures on Education (1855)

“True love is eternal, infinite, always like unto itself; it is equable, pure, without violent demonstration”

Honoré de Balzac (1799–1850) French writer

Le lys dans la vallée http://fr.wikisource.org/wiki/Le_Lys_dans_la_vall%C3%A9e (1836), translated by Katharine Prescott Wormeley, part II: First Love.
Context: True love is eternal, infinite, always like unto itself; it is equable, pure, without violent demonstration; white hair often covers the head, but the heart that holds it is ever young.

“To sustain the belief that there is no God, atheism has to demonstrate infinite knowledge, which is tantamount to saying, “I have infinite knowledge that there is no being in existence with infinite knowledge”

Ravi Zacharias (1946) Indian philosopher

“There is no doubt that we cannot do without variable quantities in the sense of the potential infinite. But from this very fact the necessity of the actual infinite can be demonstrated.”

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Georg Cantor 27

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