This e is simply the decimal point position appended to an integer x.
Scientific notation as C style output has already standardized instances like:
1.234 E 20
whereas the equivalent here will actually demolish the decimal point completely so that an integer is the remains:
123400000000000000000
which is arguably quite a large value. The crucial stance of the xe numbers are the fact that this integer form can represent values SMALLER than unity through the usage of an unsigned decimal placer (the e portion). In effect a value like
12345 E 2 (which is not the C standard notation)
as equivalent to
123.45
would suffice. We cannot place a signed value there, for these values are pre-signed. The usage of sign now comes onto the front of such a value:
s x e
and of course these form rudimentary polysign numbers. In the past I've simply written
s x
where the x is presumed to be continuous. This distinction may seem frivolous, yet from operator theory we cannot simply admit the x as real valued, or as R+, or some such nonfundamental representative. Further, the fact that the rational numbers are built as operators and values interleaved such as
3/4, 1/3, 9/5, ...
actually causes the need to now make the x portion of the sx notation better defined. Fortunately the hardware which actually performs the computations in modernity has the answers essentially built already. What is taking place here is merely an interpretation in order to dodge the ambiguity that moderners are accepting as fundamental. I no longer adhere to the real value as fundamental; polysign already had its way there long ago. Dedekind stresses over proving the continuum and lands in epsilon/delta thinking as his ultimate resting ground. That we all have absorbed this already on the irrational value which has formed the real value means that we can rest easy on all values as capable of resting just there without any of the purity that the modern mathematician claims of his rational values. This is tantamount to admitting that close enough is good enough; and that if you'd like more digits you can go chasing them all you like. Through this system of thought the values as mechanistic and radix ten without any need of further operator mechanics is essential to this interpretation being able to break away from the mixed forms of old. This is to say that the mechanics of integer operations already sufficed and that the great divide between the reals and the integers is a facade. All that is needed is the additional placer that we know in this day as a decimal point. It is to say that these decimal point versions of our numbers are still integers. Clearly they are such. Again, as I said above this is merely a matter of interpretation yet formally the distinction somewhat exposes the problems that modern mathematics faces in terms of accumulation. Should Dedekind have opted to work his proof out upon an actual value such as zz=2 we would see exactly the digit chasing procedure unfold, and the admission that under epsilon/delta that close enough is good enough. That all of our numbers should come under this roof is entirely desirable. It is a larger roof. It makes common the discrepancies that develop a subject known as real analysis. It places the mathematician as an escape artist who has thrown off physics altogether, and philosophy as well, and achieved his holy perfection... Not. No. The divorce of these subjects never was valid and never will be valid. We study reality.