I do not understand what you mean by infinity/infinity=0+/-every other number...

]]>There are different uses of the term infinity in math. Perhaps the most common is in reference to transcendental numbers. Pi for example is an infinite decimal expression, but as a distance it's not ∞. It exists somewhere between 3 and 4. Pi is a finite distance from 0 (even if we can't quite pin down the exact distance).

When I refer to ∞ I mean the farthest possible distance from 0.

0 is the lower limit, ∞ is the upper limit. (think radial or scalar dimension)

0 * 0 = 0 (can't get any smaller)

∞ * ∞ = ∞ (can't get any larger)

Like 0, ∞ is non-polar. +∞ and -∞ are the same thing. If there is a way for +∞ and -∞ to be distinct, there also must be a way for +0 and -0 to be distinct (which there might well be but I'm not willing to get into that much detail just yet).

As measured from 0 to the tangent, ∞/∞ = 0 ± 1. Details here, because words alone don't do it justice: [ http://www.perspectiveinfinity.com/root_grid.html#infdivinf ]

0 * ∞ offers a similar result but exists 90 degrees from ∞/∞ on the unit circle. *All points on the unit circle can be understood as distinct fractional representations of ±1*.

In addition to 0 ± 1, ∞/∞ *also *= 0 ± *every other natural number*. From an xy perspective when tangent is parallel with the x axis, *∞/∞ results in the entire y-axis*. Only by measuring to specific tangents can we limit the result, such as is the case with 0 ± 1.

0 is an origin. When we count from 0, everything is relative to 0. We don't preface every number with 0+ or 0-, even though that's exactly what we're doing. ∞ can also be used as an origin. Now instead of counting from 0 towards ∞ we can count from ∞ towards 0. ∞ + 1 is a finite distance from ∞, but as far as 0 is concerned ∞ + 1 = ∞. Different perspectives, different answers.

I refer to ∞ along with numbers relative to ∞ as "shadow numbers" since ∞ is not considered a "real number".

Also:

∞ + ∞ = ∞

∞ - ∞ = ∞

Remember, *non-polar*! Like zero, infinity is timeless, non-dualistic. Try splitting something timeless into finite parts and all we split is our perception of it.

Nothing is undefined.

]]>I am questioning its invalidity.

So you think I've made a valid set of axioms. hhhhmmmmm!

Bob

]]>Hi Bob;

I think you see the problem. You defined a system consisting of only 3 axioms and people are already questioning its validity. Imagine mathematics with its thousands of theorems and axioms.

Quite the opposite. I am questioning its invalidity.

]]>I think you see the problem. You defined a system consisting of only 3 axioms and people are already questioning its validity. Imagine mathematics with its thousands of theorems and axioms.

]]>a + a = c

a + a = a + a so if you substitute using axioms 1 and 2 you get

b = c which contradicts axiom 3.

You don't need commutativity or transitivity. I may choose to have them. But maybe not. They're my axioms after all.

Bob

]]>I wasn't advancing it a full theory of anything.

Actually, it's the rules for substitution that are missing.

Bob

]]>axiom 1. a + a = b

axiom 2. a + a = c

axiom 3. b ≠ c

I don't wish to be a stick in the mud, but that set of axioms is not incosistent, because you haven't defined + to be either commutative or transitive.

]]>I agree. After all math is a language. We don't have to speak the language if we don't want to. Or we can use only the parts of the language that we choose. It all depends on our individual axioms of choice.

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