Its status as a number, though, is ambiguous.
Almost all numbers follow the principle that if you multiply two of them, (excluding 0 and infinity), then change either and multiply again, there will be a different answer. However all numbers, (by common understanding), when multiplied by zero or divided by infinity, equal zero ; and all numbers, (conventionally), when multiplied by infinity or divided by zero equal infinity. Further : Consider the statement 4 = 7, (false). As algebraic laws are designed to preserve truth, (and it's true that that statement is false), there should be no way to render that statement true, (turn lead into gold). Multiplying both sides by 0 yields 0 = 0, (by common understanding), a truth, (provided zero has a definable value). If so, it's a singular kind of truth. The operation has annulled the original values and there's no way of getting back to the original statement ; (a similar, though inverse, operation can be performed with infinity, under, as before, the common understanding). As no other numbers work this way, it may be better to think of these as concepts : one of which, (0), can be located, and the other, (infinity, conventionally), cannot. By convention, those operations which result in a locatable, (zero), outcome are allowed, those which result in an unlocatable outcome, (infinity), are not. The simplification often works : results are both accurate and locatable in a linear space. However, mathematics may point toward a different understanding : Please consider the graph above. Reading from left to right, a curve comes in from the west, when x values are negative and large, (-8), and y values are negative and small (-1/8). Centering on -1,-1 it turns to the south and leaves -- temporarily -- at (-1/8, -8). These limbs can be continued in the mind to ± ∞ and 1/∞. Then it appears from the north, and in a reflection of its southwest limb, leaves to the east. It is a first-degree function that, in order to be contiguous on a flat number plane, must take all values between positive and negative infinity when x equals zero ; or, which must pass through infinity as an antipole to zero on a spherical number plane, making a circuit of its world. There is a ramification to this: positive and negative infinity would be the same place, (or infinitesimally separated), in different directions : No matter what bearing a function took, infinity would be half a globe away. If infinity remains immeasurably large, the globe would be too -- and appear flat for most purposes. But even if it's not, i think there is a relationship between its value and zero . |
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Zero equals one divided by infinity. This is implied in the function's leaving to the East and returning from the West. When x equals infinity, y will be 0 . |
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Infinity equals one divided by zero. This is implied in the function's leaving to the South and returning from the North. When x equals zero, y will be infinity . |
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Zero times infinity equals one. This can be derived from either of the previous two equations . |
| Returning to earlier examples : Multiplying a number, (7) and a redefined zero yields 7/∞. Changing 7 to 8 yields 8/∞. Different inputs bring different results . |
| And the preservation of falsehood? (quite a statement in itself) |  |
Good |
This does not completely eliminate the problem of a void at the origin. By the above formulas, ±0 are two distinct, (though infinitesimally close), values between which there really is a hole in the center of things. In other words, positive zero plus negative zero equals void. It is also imaginable that if infinity is brought down to earth and assigned a value of 10, say, so that 0 would be 1/10 -- any number that didn't divide by 1/10, 1/9, 1/8, 1/7, 1/6, 1/5, 1/4, 1/3 or1/2 would not be applicable. "Quantum-sphere mathematics" would be a form for special situations. Infinity is usually immeasurably large, making one divided by infinity immeasurably small, making the problem moot . But there is one application where bringing infinity down -- all the way down -- may answer a fine question. I'm not a physicist -- so I can't say how much application it has to this reality ; but believe that nature follows the path sensible to it . |
A Creation Myth
Imagine a void, and that the principles of math will apply there, once they have something to apply to .
The question might be asked: "In a perfect void, is there anything to prevent a possibility from expressing itself?"
Or, to put it another way: "If everything equals nothing, nothing equals everything" .
At some place in the void there emerges quantum sphere where infinity is equal to zero .
Really it's more a location than an object -- there's nothing actually there but potential .
Defining zero in terms of infinity frees it from a fixed, (null), value .
Although, it is strange to see zero exceed the value just given to infinity .
At positive or negative one, zero's value points outside the sphere. (The sphere does not exist yet) .
_
Checking back on infinity :
Mathematically, (if the model is valid), expansion would be instantaneous .
The quantum sphere, assigned an infinity 0, at once gains an infinity of ±1 . As those are zero's values too, (please see below), the system begins with them sharing identity ~ which i find philosophically interesting . |
A Quiet Moment |
At this point, within these rules, such a conjectural universe would be an enigma . Nothing between plus and minus zero would exist and zero is the same as infinity . |
If expansion continues, and if the value of ∞ must increase by whole numbers, its next would be 2 . _ Solving for 0 : |
That brings the situation out of that part of the conceptual woods .
The value of infinity is 2, distinct from and larger than the value of zero : 1/2 . When infinity becomes 3, zero would be 1/3; 4 begets 1/4, and so on... _ _ Also emerging within the universe is time : A past where the radius was smaller, and an implicit future where the radius will be larger . Space, (as i believe others have proposed in their own models), would be developed on the expanding surface of the sphere . _ _ _ _ There are intriguing issues within the model : _ Because of the irrational, (2πr), relationship between a sphere's circumference and its radius, the age and size of the universe can not both have a whole number value in the same, constant, units . In a non-quantized spacetime this could easier to handle. _ The incremental, counting-number approach to this sphere's expansion would produce a universe whose expansion slowed over time, (relative to its size) . However, observations have it that the universal expansion is accelerating, (at least in constant terms as we see them) . One, possibly incomplete or flawed means of beginning to address this is proposed below : |
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The expanding net above gives up constant measures in favor of what could be called "size levels" . Each radial step is equal to the sweep of a segment of the inner of the circumferences it touches . ( The inner three sides of each box are the same length. ) _ From the perspective of a step : the (radial) passage of time and the (circumferential) basis for the expansion (of the universe represented) could be measured in the same units to yield a rational result ; (but the expanded, larger universe could not be divided by its previous, smaller size that way) . In such a model, the expansion of the universe accelerates . |
| Photon Conjecture | On Coincidence & more |