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What is the opposite of "infinitesimal"?

Infinitesimal means a value smaller than the minimum possible measurement. For example, if we have a ruler with 1 centimeter intervals, then any length measured shorter than 1 cm is infinitesimal for that measuring instrument - smaller than the smallest possible measurement, but still greater than zero.

The opposite of infinitesimal means a value larger than the maximum possible measurement. Analogously, if we have a 100 centimeter ruler, then any length measured longer than 100 cm is that opposite term.

"Infinite" is not the opposite of infinitesimal, although that term is commonly (mis)used. Infinity is an abstract concept for something that never ends, not merely a value above measuring capability. For example, the question "how long is this road?" may have the answer "the opposite of infinitesimal" if we lack the capacity to travel along a straight road in its entirety and measure its length. On the other hand, if the road is short enough to see in its entirety but loops in on itself, we could say that its length is "infinite".

A term I came up with for this is "supermaximum"; above the maximum possible measured value. I would like to know if an official term exists.

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Where do you get that definition for "infinitesimal"? Anyway; immeasureable: "too large, extensive, or extreme to measure" – Peter Shor Feb 27 at 2:03
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Infinitesimal can be used as a noun for a mathematical concept, and then its opposite is indeed an infinity. Even when it is used as an adjective it can have this mathematical meaning. I'm not sure where your definition is from, I don't see it anywhere. – HodofHod Feb 27 at 2:13
My definition of infinitesimal is pretty much from Wikipedia. – Core Xii Feb 27 at 2:18
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If I had a 100 cm ruler, I think I could figure out how to measure longer distances with it. – Jim Feb 27 at 2:25
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If you consult Wiktionary instead, you will see that you are using an informal usage of the word, and that technically, infinitesimal is actually the opposite of infinite. – HodofHod Feb 27 at 2:29

3 Answers

up vote 8 down vote accepted

I believe that infinite is the opposite of infinitesimal.

Infinite : extending beyond, lying beyond, or being greater than any preassigned finite value however large

Infinitesimal : taking on values arbitrarily close to but greater than zero

So while infinitesimal talks about values arbitrarily smaller than any finite value but greater than zero, infinite talks about values that are arbitrarily larger than any finite value however large.

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Hm, perhaps the question is actually more philosophical than linguistic. – Core Xii Feb 27 at 4:10
up vote 4 down vote

The simple term I would use is immeasurable.

adjective
too large, extensive, or extreme to measure:
immeasurable suffering

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"Immeasurable" encompasses both infinitesimal and its opposite term. "Immeasurable" does not communicate whether the value is too small or too large to be measured; merely that it cannot be measured. – Core Xii Feb 27 at 2:15
But without measure is typically only used when conveying extremely large – Jim Feb 27 at 2:23
Although something can be immeasurably small, every dictionary (and common use) suggests that the meaning defaults to being too large. – Josh Feb 27 at 2:34
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@Core Xii: The word immeasurable cannot mean infinitesimal. Maybe you're confusing it with unmeasureable. – Peter Shor Feb 27 at 14:51
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Measureless or immeasurable. Synonyms of immense.

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Oops. I didn't see Josh's post. – Jim Feb 27 at 2:22

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