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Kasner used it to illustrate the difference between an unimaginably large number and infinity, and in this role it is sometimes used in teaching mathematics. To put in perspective the size of a googol, the mass of an electron, just under 10 −30 kg, can be compared to the mass of the visible universe, estimated at between 10 50 and 10 60 kg. [ 5 ]
A quaternion that equals its real part (that is, its vector part is zero) is called a scalar or real quaternion, and is identified with the corresponding real number. That is, the real numbers are embedded in the quaternions.
A typical book can be printed with 10 6 zeros (around 400 pages with 50 lines per page and 50 zeros per line). Therefore, it requires 10 94 such books to print all the zeros of a googolplex (that is, printing a googol zeros). [4] If each book had a mass of 100 grams, all of them would have a total mass of 10 93 kilograms.
Quadrillion Thousand billion Billiard P Peta-5 3 10 18: Quintillion Trillion Trillion E Exa-6 3 10 21: Sextillion Thousand trillion Trilliard Z Zetta-7 4 10 24: Septillion Quadrillion Quadrillion Y Yotta-8 4 10 27: Octillion Thousand quadrillion Quadrilliard R Ronna-9 5 10 30: Nonillion Quintillion Quintillion Q Quetta-10 5 10 33: Decillion ...
The number of cells in the human body (estimated at 3.72 × 10 13), or 37.2 trillion/37.2 T [3] The number of bits on a computer hard disk (as of 2024, typically about 10 13, 1–2 TB), or 10 trillion/10T; The number of neuronal connections in the human brain (estimated at 10 14), or 100 trillion/100 T
[contradictory] For example, the number 4 000 000 has a logarithm (in base 10) of 6.602; its order of magnitude is 6. When truncating, a number of this order of magnitude is between 10 6 and 10 7. In a similar example, with the phrase "seven-figure income", the order of magnitude is the number of figures minus one, so it is very easily ...
In mathematics, more specifically in the field of analytic number theory, a Landau–Siegel zero or simply Siegel zero, also known as exceptional zero [1]), named after Edmund Landau and Carl Ludwig Siegel, is a type of potential counterexample to the generalized Riemann hypothesis, on the zeros of Dirichlet L-functions associated to quadratic number fields.
In this case a point that is neither a pole nor a zero is viewed as a pole (or zero) of order 0. A meromorphic function may have infinitely many zeros and poles. This is the case for the gamma function (see the image in the infobox), which is meromorphic in the whole complex plane, and has a simple pole at every non-positive integer.