directional infinity

[AntonioLao]

Infinity as a number makes no mathematical sense. It is equivalent to the undefined term 1 divided 0. On the other hand, in the theory of limits, 0 divided by 0 is commonly known as an ‘indeterminate’ term following L’Hospital’s Rule. The rule allows the determination of derivatives and promotes the mathematics of differential calculus. However, directional infinity makes a plausible physical sense. Furthermore, it describes certain spacetime continuum.

A 3 dimensions quantity with both attributes of direction and magnitude is defined as a vector. Higher dimensional vectors are called tensors. Where and when infinite dimensions of direction implies a true spacetime continuum. On the other hand, if this infinite number of directions is quantized at the local infinitesimal spacetime of a Klein bottle, the result is a doubly infinite Hopf topology. One topology describes a yin-spacetime (H+) and the other describes a yang-spacetime (H-). Both combined topologies describe an elementary particle of neutrinos. Hence, within a single neutrino lies the topology of double infinity.

[Profpat]

And yet we use the concepts of infinity, eternity, virtual particles, etc. in our physical models as if they really exist. It makes me question the whole concept of reality itself and how real it is.

[Profpat]

Infinity as a never ending sequential numbering system makes sense. And given that infinity never ends you can never reach infinity.

[AntonioLao]

the whole concept of reality itself

Reality in my mind is doubly infinite in line with the mathematical definition of Cantor's infinities. He proved that between 0 and 1 lies an infinite number of irrational numbers with nonterminating and nonrepeating decimals.

[Profpat]

Reality in my mind is doubly infinite in line with the mathematical definition of Cantor's infinities. He proved that between 0 and 1 lies an infinite number of irrational numbers with nonterminating and nonrepeating decimals.

I remember in the book 123..infinity, there was a discussion of different types of infinities. ie the infinity of whole numbers, greater is the infinity of fractions, points and I think the last and greatest infinity was one of curves. Do you know what I'm talking about?

[AntonioLao]

Gamow wrote 123 infinity with its content as
Table of Contents for
One Two Three...Infinity: Facts and Speculations of Science

PART 1. PLAYING WITH NUMBERS I. Big Numbers 3 II. Natural and Artificial Numbers 24 PART II. SPACE, TIME & EINSTEIN III. Unusual Properties of Space 41 IV. The World of Four Dimensions 64 V. Relativity of Space and Time 84 PART III. MICROCOSMOS VI. Descending Staircase 115 VII. Modern Alchemy 149 VIII. The Law of Disorder 192 IX. The Riddle of Life 231 PART IV. MACROCOSMOS X. Expanding Horizons 269 XI. The Days of Creation 298 Index 336

Maybe he was not aware that only directional infinity is a continuum of spacetime?