03/26/2008, 12:50 AM
(This post was last modified: 03/26/2008, 01:19 AM by James Knight.)

I think the Delta Numbers are elements of the hyperreal sets. In addition, I think that Deltation will revolutionize calculus once it has been well defined. I don't think anymore that deltation values are complex or undefined, but are either infinitely far or infinitesimally close to all real numbers. I think that it is rather interesting that the delta symbol was chosen to represent deltatation as it has to do with calculus and infinitesimal quantities. I am beginng to wonder whether or not hyper real positive vs negative quantites exist. (ie does positive and negative infinity mean the same thing?)

Deltation -> Hyper Real Infinite and Infinitesimal

Subtraction -> Integer Negative Numbers

Division -> Rational Fractions

Roots and Logarithms -> Irrational and Complex/Imaginary

etc.

Notice how you cant produce the "new" number type in a previous level without using that number type.

ie. you can't get a rational number by subtracting two integers

ie. you can't get an irrational number by diving two rationals

I'm not saying you can't have negative infity, but what I am asking is whether you can result negative infinity from deltation?

so can a hyper real really be infinitely negative when negativity doesn't exist in the natural number set

Possibly, because Knightation subtracts so it might produce negative numbers... (also a better name for Knightation might me Jeration... )

I am also pondering when in Knightation whether there a limit to how far back you can go like with logarithms. (ie you can't take the logarithm of zero. This would mean an asymptotic relationship for zeration and knightation. This might be something to look in to.

Well, I think I got my post quota for today!

James

Deltation -> Hyper Real Infinite and Infinitesimal

Subtraction -> Integer Negative Numbers

Division -> Rational Fractions

Roots and Logarithms -> Irrational and Complex/Imaginary

etc.

Notice how you cant produce the "new" number type in a previous level without using that number type.

ie. you can't get a rational number by subtracting two integers

ie. you can't get an irrational number by diving two rationals

I'm not saying you can't have negative infity, but what I am asking is whether you can result negative infinity from deltation?

so can a hyper real really be infinitely negative when negativity doesn't exist in the natural number set

Possibly, because Knightation subtracts so it might produce negative numbers... (also a better name for Knightation might me Jeration... )

I am also pondering when in Knightation whether there a limit to how far back you can go like with logarithms. (ie you can't take the logarithm of zero. This would mean an asymptotic relationship for zeration and knightation. This might be something to look in to.

Well, I think I got my post quota for today!

James