Infinitesimal vs. Infinity — What's the Difference?

In mathematics, an infinitesimal or infinitesimal number is a quantity that is closer to zero than any standard real number, but that is not zero. The word infinitesimal comes from a 17th-century Modern Latin coinage infinitesimus, which originally referred to the "infinity-th" item in a sequence.

Infinity is that which is boundless or endless, or something that is larger than any real or natural number. It is often denoted by the infinity symbol shown here.

Immeasurably or incalculably minute.

The state or quality of being infinite

(Mathematics) Capable of having values approaching zero as a limit.

A number greater than any assignable quantity or countable number (symbol ∞)

An immeasurably or incalculably minute amount or quantity.

The quality or condition of being infinite.

(Mathematics) A function or variable continuously approaching zero as a limit.

Unbounded space, time, or quantity.

Incalculably, exceedingly, or immeasurably minute; vanishingly small.

An indefinitely large number or amount.

(mathematics) Of or pertaining to values that approach zero as a limit.

(Mathematics) The limit that a function  is said to approach at x = a when (x) is larger than any preassigned number for all x sufficiently near a.

(informal) Very small.

A range in relation to an optical system, such as a camera lens, representing distances great enough that light rays reflected from objects within the range may be regarded as parallel.

(mathematics) A non-zero quantity whose magnitude is smaller than any positive number (by definition it is not a real number).

A distance setting, as on a camera, beyond which the entire field is in focus.

Infinitely or indefinitely small; less than any assignable quantity or value; very small.

(uncountable) endlessness, unlimitedness, absence of a beginning, end or limits to size.

An infinitely small quantity; that which is less than any assignable quantity.

A number that has an infinite numerical value that cannot be counted.

Infinitely or immeasurably small;

An idealised point which is said to be approached by sequences of values whose magnitudes increase without bound.

(uncountable) A number which is very large compared to some characteristic number. For example, in optics, an object which is much further away than the focal length of a lens is said to be "at infinity", as the distance of the image from the lens varies very little as the distance increases further.

The symbol ∞. Category:en:Infinity

Unlimited extent of time, space, or quantity; eternity; boundlessness; immensity.

Unlimited capacity, energy, excellence, or knowledge; as, the infinity of God and his perfections.

Endless or indefinite number; great multitude; as an infinity of beauties.

A quantity greater than any assignable quantity of the same kind.

That part of a line, or of a plane, or of space, which is infinitely distant. In modern geometry, parallel lines or planes are sometimes treated as lines or planes meeting at infinity.

Time without end