Georg Cantor quote: “The potential infinite means nothing other than an undetermined, variable quantity, always remaining finite, which has …”

“When… we have a series of values of a quantity which continually diminish, and in such a way, that name any quantity we may, however small, all the values, after a certain value, are severally less than that quantity, then the symbol by which the values are denoted is said to diminish without limit. And if the series of values increase in succession, so that name any quantity we may, however great, all after a certain point will be greater, then the series is said to increase without limit. It is also frequently said, when a quantity diminishes without limit, that it has nothing, zero or 0, for its limit: and that when it increases without limit it has infinity or ∞ or 1⁄0 for its limit.”

Augustus De Morgan (1806–1871) British mathematician, philosopher and university teacher (1806-1871)

Introductory Chapter, pp.9-10
The Differential and Integral Calculus (1836)

“Because they [the ancient Greeks] feared infinite processes they missed the limit process. In approximating a circle by a polygon they were content to make the difference smaller than any given quantity, but something positive was always left over. Thus the process remained clear to the intuition; the limit process, on the other hand, would have involved the infinitely small.”

Morris Kline (1908–1992) American mathematician

Source: Mathematical Thought from Ancient to Modern Times (1972), p. 176

“The infinite of the soul is mightier than the finite in it.”

George Holmes Howison (1834–1916) American philosopher

Source: The Limits of Evolution, and Other Essays, Illustrating the Metaphysical Theory of Personal Ideaalism (1905), The Harmony of Determinism and Freedom, p.373

“A ring of polynomials in any number of variables over a ring of coeffcients that has an identity element and a finite basis, itself has a finite basis.”

Emmy Noether (1882–1935) German mathematician

As quoted in Morris Kline, Mathematical Thought From Ancient to Modern Times (1972) p. 1153.

“For how shall the finite comprehend the infinite?”

Baruch Spinoza (1632–1677) Dutch philosopher

George Boole, An Investigation of the Laws of Thought (1854) Ch. 13. Clarke and Spinoza, pp. 216-217. https://books.google.com/books?id=DqwAAAAAcAAJ&pg=PA216
Context: It is not possible, I think, to rise from the perusal of the arguments of Clark and Spinoza without a deep conviction of the futility of all endeavors to establish, entirely à priori, the existence of an Infinite Being, His attributes, and His relation to the universe. The fundamental principle of all such speculations, viz. that whatever we can clearly conceive, must exist, fails to accomplish its end, even when its truth is admitted. For how shall the finite comprehend the infinite? Yet must the possibility of such conception be granted, and in something more than the sense of a mere withdrawal of the limits of phænomal existence, before any solid ground can be established for the knowledge, à priori, of things infinite and eternal.

“Thesis. Finite, Representable. Antithesis. Infinite, System of Notions lying at the limit of the representable.”

Bernhard Riemann (1826–1866) German mathematician

Antimonies
Gesammelte Mathematische Werke (1876)

“When… we have a series of values of a quantity which continually diminish, and in such a way, that name any quantity we may, however small, all the values, after a certain value, are severally less than that quantity, then the symbol by which the values are denoted is said to diminish without limit. And if the series of values increase in succession, so that name any quantity we may, however great, all after a certain point will be greater, then the series is said to increase without limit.”

Augustus De Morgan (1806–1871) British mathematician, philosopher and university teacher (1806-1871)

It is also frequently said, when a quantity diminishes without limit, that it has nothing, zero or 0, for its limit: and that when it increases without limit it has infinity or ∞ or 1&frasl;0 for its limit.
The Differential and Integral Calculus (1836)

“The infinite being has assumed unto himself the mystery of finitude. And in him who is love the finite and the infinite are made one.”

Rabindranath Tagore (1861–1941) Bengali polymath

Sādhanā : The Realisation of Life http://www.spiritualbee.com/spiritual-book-by-tagore/ (1916)
Context: In love, at one of its poles you find the personal, and at the other the impersonal. At one you have the positive assertion — Here I am; at the other the equally strong denial — I am not. Without this ego what is love? And again, with only this ego how can love be possible?
Bondage and liberation are not antagonistic in love. For love is most free and at the same time most bound. If God were absolutely free there would be no creation. The infinite being has assumed unto himself the mystery of finitude. And in him who is love the finite and the infinite are made one.

“For man to be able to live he must either not see the infinite, or have such an explanation of the meaning of life as will connect the finite with the infinite.”

Leo Tolstoy (1828–1910) Russian writer

Source: Confession (1882), Ch. 9

“you and I have good enough minds to know how very limited and finite they really are. The naked intellect is an extraordinarily inaccurate instrument.”

Madeleine L'Engle A Wind in the Door

Source: A Wind in the Door

“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.”

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Georg Cantor 27

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