The concept of the infinitely small is involved in the relation of points to a line or the relation of the discrete to the continuous, and Zeno's paradoxes may have caused the Greeks to shy away from this subject.

After these came to be relished, an infinite scale of infinites and s (ascending and descending always by infinite steps) was imagined and proposed to be received into geometry, as of the greatest use for penetrating into its abstruse parts. Some have argued for quantities more than infinite; and others for a kind of quantities that are said to be neither finite nor infinite, but of an intermediate and indeterminate nature.

As for the mathematical infinite, to the extent that it has found a justified application in science and contributed to its usefulness, it seems to me that it has hitherto appeared principally in the role of a variable quantity, which either grows beyond all bounds or diminishes to any desired minuteness, but always remains finite. I call this the improper infinite [das Uneigentlich-unendliche].

Infinity...is used in physics simply as a shorthand for "a very big number.”

Zero invites imagination, but small numbers invite questions about whether large numbers will ever materialize.

Infinity is the land of mathematical hocus pocus. There Zero the magician is king. When Zero divides any number he changes it without regard to its magnitude into the infinitely small [great?], and inversely, when divided by any number he begets the infinitely great [small?]. In this domain the circumference of the circle becomes a straight line, and then the circle can be squared. Here all ranks are abolished, for Zero reduces everything to the same level one way or another. Happy is the kingdom where Zero rules!

The role of the infinitely small in nature is infinitely great.

The infinitely small have a pride infinitely great.

The ratio of something to nothing is infinite.

Whether we see it or not, It is manifest everywhere in all the ten quarters. Infinitely small things are as large as large things can be, For here no external conditions obtain; Infinitely large things are as small as small things can be, For objective limits are here of no consideration. What is is the same as what is not, What is not is the same as what is: Where this state of things fails to obtain, Indeed, no tarrying there. One in All, All in One — If only this is realized, No more worry about your not being perfect! Where Mind and each believing mind are not divided, And undivided are each believing mind and Mind, This is where words fail; For it is not of the past, present, and future.

Statements like ‘a quantity x has a completely definite value’ (expressed by a real number and represented by a point in the mathematical continuum) seem to me to have no physical meaning.

All things were together, infinite both in number and in smallness; for the small too was infinite.

I protest against the use of infinite magnitude as something completed, which is never permissible in mathematics. Infinity is merely a way of speaking

Every quantity is intellectually conceivable as infinitely divisible.