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Intervals: terminology and symbols

This is a little bit esoteric and mathematical perhaps but I keep forgetting the symbols

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An interval for these purposes is a span of values and it is often defined by limits, for example in the UK and many countries an adult is someone who is 18 years or older: age >= 18. That has a cut-off point but no clear upper limit. The internet tells me that the current record for human age is 122 years and 164 for the rather bizarre life of Jeanne Calment: https://en.wikipedia.org/wiki/Jeanne_Calment, however presumably if we wait long enough someone will live longer than she did so I think the upper bound or limit is infinity (∞) though I think that’s a purely theoretical upper limit.

The intervals for younger ages like “infant”, “child”, “adolescent” are multiple and I think they are not legally defined (“infanticide” is but let’s sidestep that). However, I think even “infant” doesn’t include zero age so “not an adult” (in the UK) could be defined by age in years as 0 < age in years < 18 and mathematicians write that as “(0, 18)” where “(” is the symbol for an excluded lower limit. (That is the bit I seem never to remember.) The excluded upper limit symbol is “)”. The definition of a UK adult is age >= 18 and as a mathematical interval I think that becomes the theoretical “[18, ∞]” which shows the that the symbols for the lower and upper included values/limits are “[” and “]” respectively.

For mathematicians that definition of an adult is a “left bounded interval”: the bottom limit is included but the top is infinity so it is not defined. For a “bounded interval” both limits are included. The decimal digits are truly bounded interval “[0, 9]”.

Just as infiinity is a rather odd thing, mathematicians think that 1 is a bit different from other integers and they call an interval with only one included value a “degenerate interval”. Fair enough: it’s clearly not an interval.

OK, I think I’ve got that off my chest and maybe I will now remember the correct usage of “(“, “)”, “[” and “]”.

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Not covered in the OMbook.

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None feasible I think!!

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First created 13.iv.25.

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