_(-1) is a strange number arising from Underscore Theory. In underscore theory we have a function _(a) where a is any ordinal number. _(0) = 0 by definition. By convention we use _ = _(1). The properties of underscores are simple:
_a * _b = _max(a,b)
The product always returns the larger of the two indexes. So for 0 * _ we have:
_0 * _1 = _1 = _
or we could say _5 * _3 = _5
etc.
Hyper-zeroes can be generated in this way using the underscore notation. Underscore numbers are assumed to have the following additional properties:
_a * x = _a : min(_a,x) = _a
That is, these elements can not be made smaller or larger by multiplication unless x is smaller than _a. They are assumed to form discrete levels of smallness.
We now postulate the existence of _(-1). By our rule _(-1) * 0 = 0. This implies _(-1) is greater than 0 ... and yet:
_(-1) * 0.000000001 = _(-1), and _(-1) * _(-1) = _(-1)
This number otherwise acts like 0. This implies it is smaller than any positive real number. It should also be smaller than any infinitesimal as well, yet it is somehow larger than 0. _(-1) is a special type of number known as a megalo-zero. It is similar to sqrt(*0). Let's say we assume that _(-1) is the square root of 0. This implies _(-1)^2 = 0. However _(-1) * _(-1) = _(-1). The product of _(-1) with itself is itself, a common property held by all underscore numbers. Therefore it is not the sqrt(*0). It is believed that _(-1) is larger than the sqrt(*0) in much the same way that _ is smaller than *0^2.