07/31/2009, 07:20 AM
(This post was last modified: 07/31/2009, 07:31 AM by mathamateur.)

(07/30/2009, 11:40 PM)Tetratophile Wrote:(07/30/2009, 06:21 PM)mathamateur Wrote: of course -oo and +oo is a number. Are you saying 0 is not a number? its 1/oo and -1/oo. you can make -oo a number since its 0-oo and 0-delta oo.

tell me your thoughts

the infinities are not (normally) considered numbers (that you can treat like ordinary numbers) because if you do, you lose some important algebraic properties. There are extensions of real and complex numbers to include infinity/ies. The "extended number line" has the positive and the negative infinity you want. The "real projective line" tapes the two infinities together to make it one infinity. But you still cant do infinity - infinity. Also you don't know if 1/0 is positive or negative unless there are both positive and negative zeros. Actually it's neither. infinity doesn't behave like numbers all the time, so mathematicians just like to be careful.

But for a simple operation like deltation, it may be useful to treat it like a "zerative" identlty. Some info on limiting values of zeration may be needed tho.

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Thanks, interesting thoughts to ponder. Now i've heard a suggestion that -oo for zeration ought to get a new symbol, a zero with a line through it. That makes me think that you can actually reach negative infinity just line one can reach zero even though fractions go on getting smaller forever.

Maybe +infinity is the only "number-type symbol" that can't be reached. We have delta numbers before -oo, but nothing after +oo or even +ooi. unless some s=? operation can create it.

(03/26/2008, 12:50 AM)James Knight Wrote: 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?

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Sure you can result -oo from deltation. I think the order of things goes backwards in terms of hyperoperations. division creates fractions below one (approaches zero). subtraction creates negative numbers below zero (approaches -00). then delation creates numbers below -infinity (approaches delta +infinity). goes from s=2 to s=1 to s=0

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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

(03/26/2008, 12:50 AM)James Knight Wrote: 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

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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?

----

Sure you can result -oo from deltation. I think the order of things goes backwards in terms of hyperoperations. division creates fractions below one (approaches zero). subtraction creates negative numbers below zero (approaches -00). then delation creates numbers below -infinity (approaches delta +infinity). goes from s=2 to s=1 to s=0

-mathamateur