Consider an infinite plain, from a to b, without recourse or stop, we can say according to phsyical math as:
∞=[∞-(-∞)]²
Which has the coordinates:
(-∞,∞) x (-∞,∞)
Which then suggests it must have an infinite plain - by simplifying ∞=[∞-(-∞)]² we get;
∞=(2∞)²
And so
∞=4∞²
Which must give since according to prove ∞=[∞-(-∞)]²
b
∫ =f(t) dt=∞
a
Easily states that f(t) does not have a boundary Ω between a and b, so it must imply some infinite range. We should now consider a second infinite plane, which would allow us to calculate one infinite plain which is incoming, and a second which is outgoing. We could express this as:
x<z<z
x>y>z
(If we simply replace the x and z coordinates here with infinities, we find one infinity ascending in the positive direction, we find another descending in the opposite.
Thus instead of just saying, (1) ∞→-∞, we also have (2) -∞→∞, and so now I suppose each plain, call (1) the conjugate of plain (2). This assigns each plain a special property which equally relates the two. If plain (1) acts as a boundary to plain (2) upon mathematical cobjugation, we actually find the following:
b
∫ =f(t) dt=∞
a
and
-b
∫ =f(t) dt=-∞
-a
So that the boundary of |∞|² given as the absolute square of the infinities in question, which is analogous to -∞•∞ where one can consider some renormalization, since being conjugates, one could have the value 1. The only problem one would consider here, is that the mathematical expression -∞•∞ yields normally undefined, because -∞•∞ should yield simply -∞. But perhaps infinite qualities (but only certain kinds as acting like conjugates of each other), could break the mathematical dogma?
My thoughts remind me of Cantors proof of infinities showing that one infinity can be larger than another infinity which initially suggests some countable difference between the two elements. If two infinities as quickly shown:
Lim of (n →∞)^n =∞
And
Lim of (n →∞)^n² =∞
(1)
Where Lim of n →∞^n² =∞ implies a greater infinity than Lim of n →∞^n =∞, then we may be able to have two infinities, one moving in the positive direction and the other moving in the negative direction to both have values which together yield a single finite value may be possible. It could help maybe by mathematical notation that ∞=(a+bi) and ∞=(a-bi) (2), where the two of them multipled would yield some real positive answer.
(1)- This is like saying that:
(∞∑ of n=1)^n≠(∞∑ of n=1)^n²
But in the end, this is just one way to show his infinities to not equal the same value, but its not the tradiational way, i know, i just require some descretion.
(1) - Whilst infinities cannot be respresented as (x+yi), there must be some way to treat one infinity as a conjugate to another, unless i am specifically missing a rule of math?
My Question
I have studied the fallacies of mathematics for a few years now, and I always here you cannot subtract an infinity from another, unless you do not define one not being a little larger than the other in some arbitrary way, likewise, you can’t divide them unless you specify the qualities, as Cantor once proved. So now I ask, why can one not define a real finite value, unless this value was calculated by multiplying two infinities acting as conjugates of each other, where there is some boundary upon contact, much like how one might envision the infinite wave function collapsing upon some measurement? So in another set of words, why can’t we define two infinities by multiplication if they have properties which can cancel, but not maybe completely, their own internal properties?
∞=[∞-(-∞)]²
Which has the coordinates:
(-∞,∞) x (-∞,∞)
Which then suggests it must have an infinite plain - by simplifying ∞=[∞-(-∞)]² we get;
∞=(2∞)²
And so
∞=4∞²
Which must give since according to prove ∞=[∞-(-∞)]²
b
∫ =f(t) dt=∞
a
Easily states that f(t) does not have a boundary Ω between a and b, so it must imply some infinite range. We should now consider a second infinite plane, which would allow us to calculate one infinite plain which is incoming, and a second which is outgoing. We could express this as:
x<z<z
x>y>z
(If we simply replace the x and z coordinates here with infinities, we find one infinity ascending in the positive direction, we find another descending in the opposite.
Thus instead of just saying, (1) ∞→-∞, we also have (2) -∞→∞, and so now I suppose each plain, call (1) the conjugate of plain (2). This assigns each plain a special property which equally relates the two. If plain (1) acts as a boundary to plain (2) upon mathematical cobjugation, we actually find the following:
b
∫ =f(t) dt=∞
a
and
-b
∫ =f(t) dt=-∞
-a
So that the boundary of |∞|² given as the absolute square of the infinities in question, which is analogous to -∞•∞ where one can consider some renormalization, since being conjugates, one could have the value 1. The only problem one would consider here, is that the mathematical expression -∞•∞ yields normally undefined, because -∞•∞ should yield simply -∞. But perhaps infinite qualities (but only certain kinds as acting like conjugates of each other), could break the mathematical dogma?
My thoughts remind me of Cantors proof of infinities showing that one infinity can be larger than another infinity which initially suggests some countable difference between the two elements. If two infinities as quickly shown:
Lim of (n →∞)^n =∞
And
Lim of (n →∞)^n² =∞
(1)
Where Lim of n →∞^n² =∞ implies a greater infinity than Lim of n →∞^n =∞, then we may be able to have two infinities, one moving in the positive direction and the other moving in the negative direction to both have values which together yield a single finite value may be possible. It could help maybe by mathematical notation that ∞=(a+bi) and ∞=(a-bi) (2), where the two of them multipled would yield some real positive answer.
(1)- This is like saying that:
(∞∑ of n=1)^n≠(∞∑ of n=1)^n²
But in the end, this is just one way to show his infinities to not equal the same value, but its not the tradiational way, i know, i just require some descretion.
(1) - Whilst infinities cannot be respresented as (x+yi), there must be some way to treat one infinity as a conjugate to another, unless i am specifically missing a rule of math?
My Question
I have studied the fallacies of mathematics for a few years now, and I always here you cannot subtract an infinity from another, unless you do not define one not being a little larger than the other in some arbitrary way, likewise, you can’t divide them unless you specify the qualities, as Cantor once proved. So now I ask, why can one not define a real finite value, unless this value was calculated by multiplying two infinities acting as conjugates of each other, where there is some boundary upon contact, much like how one might envision the infinite wave function collapsing upon some measurement? So in another set of words, why can’t we define two infinities by multiplication if they have properties which can cancel, but not maybe completely, their own internal properties?