Sub-poll!
- 0E0
- -1
- 2147483647
- -2147483647
- π or e or sqrt(2)
- i
- -Inf
- NaN
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Apparently, the totalOrder predicate from IEEE 754-2008 specifies that -NaN < -Inf < negative finite numbers < -0 < +0 < positive finite numbers < +Inf < +NaN.
So if floating point values are allowed, then I think that "-Nan" would be the obvious starting point ... coz you can't not get no lower than that ;-)
(Hopefully, indexes have to be real integer values.)
Cheers, Rob
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Close: my answer would have been the first index is Φ ≈ 1.618, second is e ≈ 2.718, third is π ≈ 3.14, and so on, picking irrational (and preferably transcendental) numbers whose integer portion is the next counting number. (I had forgotten that Φ, like √2, is irrational but algebraic, and had started to write that as "picking transcendental numbers" before having a long think about it; still, I prefer Φ since it has a predefined symbol.)
Ooh, another fun set: ln(2) ≈ 0.693, √2 ≈ 1.414, 2**(√2) ≈ 2.665, ... I'm sure someone could come up with a whole series of those whose integer portions are increasing, but all the terms only combine operators and 2. ;-)
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