The difference between Infinitesimal and Infinity
When used as nouns, infinitesimal means a non-zero quantity whose magnitude is smaller than any positive number (by definition it is not a real number), whereas infinity means endlessness, unlimitedness, absence of a beginning, end or limits to size.
Infinitesimal is also adjective with the meaning: incalculably, exceedingly, or immeasurably minute.
check bellow for the other definitions of Infinitesimal and Infinity
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Infinitesimal as an adjective:
Incalculably, exceedingly, or immeasurably minute; vanishingly small.
Examples:
"Do you ever get the feeling that you are but an infinitesimal speck, swallowed by the vastness of the universe and beyond?"
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Infinitesimal as an adjective (mathematics):
Of or pertaining to values that approach zero as a limit.
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Infinitesimal as an adjective (informal):
Very small.
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Infinitesimal as a noun (mathematics):
A non-zero quantity whose magnitude is smaller than any positive number (by definition it is not a real number).
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Infinity as a noun (uncountable):
Endlessness, unlimitedness, absence of a beginning, end or limits to size.
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Infinity as a noun (countable, mathematics):
A number that has an infinite numerical value that cannot be counted.
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Infinity as a noun (countable, topology, analysis):
An idealised point which is said to be approached by sequences of values whose magnitudes increase without bound.
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Infinity as a noun (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.
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Infinity as a noun (uncountable):
The symbol ∞.