identity operators

[AntonioLao]

The identity matrix might be considered as the only infinitely ordered matrix that is the inverse of itself asides from others such as Pauli spin matrices. As a matrix multiplication operator operating on itself it produces itself infinitely but its eigenvalues remain unity, analogous to the product of an infinite number of unity: 1x1x1x1x1x1x1x1x…=1. On the other hand, under the addition operator, its sum is infinity: 1+1+1+1+1+1+1+1+…=∞. Under the logarithmic operator (either common base 10 or natural base e), the log of a product of A and B is equal to the sum of each log: log(AB)=logA+logB. Then log(1)+log(1)+log(1)+log(1)+log(1)+log(1)+ log(1)+log(1)+…= log(1)=0 since the log of unity in any base is always zero. However, the law of logarithm is the inverse of the law of exponentiation for any given base and it is defined that any base raised to the power zero is always unity, for examples: eº=1, 10º=1, (-1)º=1, (½)º=1, pº=1. These imply that a zero power law applies to both positive and negative real numbers. In fact, as a simple handheld scientific calculator will show, it applies to all complex numbers as well as hypercomplex numbers: vectors, tensors, spinors, twistors, quaternions, etc.

It can be logically demonstrated that power zero of anything is unity. Given the complex number (1+i) where i is the imaginary unity, its zero power is unity: (1+i)º=1. However, its inverse is ½-½i such that the product of (1+i)( ½-½i)=1 while its conjugate product (1+i)(1-i)=2. Conjugate product normalization for complex number z=a+bi and conjugate z*=a-bi requires that a=b=±½√2 when solving the unit circle on the complex plane:a+b=1. Hence, power zero becomes a complete and total generalization of all operations under division, inverse, reciprocal, and conjugation. The most logical conclusion is that to identify anything in nature it suffices to raise it to the power zero: (everything)º=1. Then it can now be defined that the zero power of infinity is absolutely unity: ∞º=1. Likewise, it can be defined that the zero power of zero is also unity: 0º=1. In order to connect infinity to zero and zero back to infinity is simply raising both to power zero. Nonetheless, it has been proved that the average expected value of infinity is absolutely zero.

[mkirkpatrick]

Absolute zero is the Absolute in "pre thought mode"!





regards michael.

[AntonioLao]

Absolute zero is the Absolute in "pre thought mode"!

Same as the starting point of an idea? Some ideas were responsible for the greatest discoveries in both sciences and the humanities minus the destructive ones.

[mkirkpatrick]

Same as the starting point of an idea? Some ideas were responsible for the greatest discoveries in both sciences and the humanities minus the destructive ones.

Exactly my friend,and the greatest IDEA of ALL is that we are the product of it,that which
IS/.

[AntonioLao]

Would this greatest idea be the same as the true TOE?

[mkirkpatrick]

Would this greatest idea be the same as the true TOE?

Yes I think it would,what a wonderful concept to behold!




regards michael.

[bottomlander]

Same as the starting point of an idea? Some ideas were responsible for the greatest discoveries in both sciences and the humanities minus the destructive ones.

IMHO, one of the "destructive ideas" is to play tricks with "≠" = "=". This useless trick makes all elaborately derived equations in the starting message of this thread being destructed to meaningless!

Such trick only serves to bring out Big Claims to satisfy erroneous uniqueness.


Best Regards. Bottomlander