Goodbye Dr. Hawking

Dr. Stephen W. Hawking has died on the day of pi and on Albert Einstein’s birthday. 

The Theory of Everything remains to be solved.

We respect him by presenting you his Doctoral thesis (1966) made freely accessible by University of Cambridge:

Properties of Expanding Universes

Appolo (Univeristy of Cambridge)

Cambridge University Library (High Resolution)




Right to Data protection

We strongly stand against all the blood-sucking ransom-ware makers and sharers. We wish we had the power to terminate and forever block them and  their spreading. So that everyone can use,control,share and store their data in their computers.

One of our computer was infected with two different types of ransom-wares – Cryptowall 3.0 and CERBER Ransomware (07 Apr 2016). Thousands of our files were encrypted using modern AES 256 key. We don’t have the required money to decrypt and the encrypted files are not so important. But this illegal ransom-wares and viruses must be blocked.



What Is Infinity?

Infinity (symbol: ) is an abstract concept describing something without any limit and is relevant in a number of fields, predominantly mathematics and physics. In mathematics, “infinity” is often treated as if it were a number (i.e., it counts or measures things: “an infinite number of terms”) but it is not the same sort of number as natural or real numbers. In number systems incorporating infinitesimals, the reciprocal of an infinitesimal is an infinite number, i.e., a number greater than any real number.
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In real analysis, the symbol \infty, called “infinity”, is used to denote an unbounded limit. x \rightarrow \infty means that x grows without bound, and x \to -\infty means the value of x is decreasing without bound. If f(t) ≥ 0 for every t, then

  • \int_{a}^{b} \, f(t)\ dt \ = \infty means that f(t) does not bound a finite area from a to b
  • \int_{-\infty}^{\infty} \, f(t)\ dt \ = \infty means that the area under f(t) is infinite.
  • \int_{-\infty}^{\infty} \, f(t)\ dt \ = a means that the total area under f(t) is finite, and equals a

Infinity is also used to describe infinite series:

  • \sum_{i=0}^{\infty} \, f(i) = a means that the sum of the infinite series converges to some real value a.
  • \sum_{i=0}^{\infty} \, f(i) = \infty means that the sum of the infinite series diverges in the specific sense that the partial sums grow without bound.

Infinity can be used not only to define a limit but as a value in the extended real number system. Points labeled +\infty and -\infty can be added to the topological space of the real numbers, producing the two-pointcompactification of the real numbers. Adding algebraic properties to this gives us the extended real numbers. We can also treat +\infty and -\infty as the same, leading to the one-point compactification of the real numbers, which is the real projective line. Projective geometry also refers to a line at infinity in plane geometry, a plane at infinity in three-dimensional space, and so forth for higher dimensions.