Singleton Infinity vs Float Infinity

[Kevin Ventullo]

Hi,

I posted about this on GitHub but haven't gotten much of a response. Right now there are two seemingly mathematically equivalent notions of positive and negative infinity on the real line: 

-The singleton sympy.core.numbers.Infinity, also known as "oo"

-Float("inf"), also known as "+inf"

When trying to compare one of these to the other, we get inconsistent results, e.g.

-oo < -inf

will be left unevaluated but

-inf > -oo

returns False.

I guess both of these should be False. However, we also have

oo == x is False, but

x == oo is True.

Which of these is correct? Both of them?

[Kevin Ventullo]

By the way, this is not just an intellectual curiosity: right now if you ask Sympy what is the probability a uniform random variable on [0,1] (defined with Uniform) is less than 0.5, you get an error which boils down to these comparisons. See https://github.com/sympy/sympy/issues/8910

[Aaron Meurer]

This has been brought up before. See https://github.com/sympy/sympy/issues/7765 and https://github.com/sympy/sympy/issues/8451.  I don't remember if there was ever a good reason to keep Float('inf') as a separate object from oo.

Aaron Meurer

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