circular infinity

[AntonioLao]

The sine circular function which is one of the important trigonometric functions with given arguments in degrees or radians can be used to illustrate the infinitesimal calculus of circular infinity. The derivative of sin(x) is defined as cos(x), and cosine is another important complementary circular trigonometric function. However, the derivative of cos(x) is negative sin(x) such that the nth derivative of sin(x) is sin(x) if n takes the sequence of integer values: 4,8,12,16,...each succeeding number is 4 more than the previous number. The nth derivative of sin(x) is cos(x) if n takes the sequence: 1,5,9,13,…, again, each succeeding number is greater by 4. The nth derivative of sin(x) is negative sin(x) if n has the sequence: 2,6,10,14,18,…,again, the larger number is greater by 4 than its predecessor. The nth derivative of sin(x) is negative cos(x) if n has the sequence 3,7,11,15,19,…,difference of 4.

It can be easily shown that the nth derivatives of cos(x) follow similar alternating patterns of sin(x), cos(x),-sin(x), and –cos(x). Interestingly, the nth antiderivative of indefinite integrals where the integration constant is always zero follow similar reversible alternating patterns of sin(x), cos(x),-sin(x), and –cos(x). These similarities suggest certain circular infinities for both directions of differentiation and integration. The proof’s demonstrations can be carried out by term by term differentiation or integration of the alternating infinite power series expansions for both sin(x) and cos(x).

[austintorn@aol.com]

Both infinity and eternity are circular in no-origin (forever) systems because they are their own precursor, kind of running as a mobius strip or a klein bottle. Their own byproducts of the 'future' are alway ever available to then in the present and the past. For example, matter requires light, but light requires matter. A star requires some amount of compound nuclei for igniton, but that is what a star produces.

[AntonioLao]

Then circular infinity is similar to the law of the conservation of energy which states that energy cannot be destroyed or created. Nonetheless, the annihilation and creation operators of quantum field theories should then imply that only as squares of energy can matter and energy be created or destroyed.

[Nobody Nowhere]

Then circular infinity is similar to the law of the conservation of energy which states that energy cannot be destroyed or created. Nonetheless, the annihilation and creation operators of quantum field theories should then imply that only as squares of energy can matter and energy be created or destroyed.

Isn't energy already implied to be equal to matter squared? Could the Higgs' Boson be the square of neutron mass with enough energy to produce neutrons?

[PoPpAScience]

Both infinity and eternity are circular in no-origin (forever) systems because they are their own precursor, kind of running as a mobius strip or a klein bottle. Their own byproducts of the 'future' are alway ever available to then in the present and the past. For example, matter requires light, but light requires matter. A star requires some amount of compound nuclei for ignition, but that is what a star produces.

Infinity does not need to run like a "mobius strip or a klein bottle", if it just "IS"(Eternity). This is where time fools with one's mind, time is strictly "IS" changing position as perceived by Mind. There is no flow of time, just flow of change of position of "IS" in form.

[AntonioLao]

Isn't energy already implied to be equal to matter squared? Could the Higgs' Boson be the square of neutron mass with enough energy to produce neutrons?

Square of energy is implied by both the Dirac and Klein-Gordon equations for fermions and boson. The Higgs boson mass is calculated using the Higgs mechanism which I'm not familiar with and cannot give anymore information regarding its derivation.

[AntonioLao]

This is where time fools with one's mind, time is strictly "IS" changing position as perceived by Mind.

This can be separately meaningful whenever time is represented by both rational and irrational numbers. See new thread on the differences of physical and mathematical spacetime.