The Hilbert – Reimann Paradox

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  • A. B. Jithendra Department of ECE, University Visvesvarayya College of Engineering, Bengaluru, Karnataka, India


Gaussian Integral, Definite integral properties with the infinity limits, Basic mathematical concepts and properties


In this paper we introduced a method to solve the derivation towards Reimann - HiIbert's paradox. We are using the very basic concepts of Reimann - Hilbert's paradox. The basic concepts of the complex analysis and gaussian integrals, to solve the equation like $\infty - \infty = z$, where `z' is any complex constant and as we know a complex number is also a real number when it's imaginary part has zero as its co-efficient. As we know the quantity infinity is a very hard countability as well as complex mathematical concept. Many ideas that we find intuitive when working with the normal numbers don't work anymore, and instead there are countless apparent paradoxes. However, this paper clears the idea behind it. Hilbert's paradox of the grand hotel is a mathematical paradox named after the German Mathematician David Hilbert. According to the Hilbert's Grand hotel paradox, suppose consider a hotel that has an infinite number of rooms. As a convenience the rooms have numbers, the first room has a number 1, the second has number 2 and so on. If all the rooms are filled, it might appear that no more guests can be take in, as in a hotel with the finite number of rooms. This is where the statement slightly contradicts, now in the Hilbert's hotel a room can always be provided for another guest by moving the guest in room1 to room2, and the guest in room 2 to room 3 and so on. In the general case the case in guest in room number `n' is moved to room number `$n+1$'. After all the guests are moved now the room 1 is empty and the new guest can occupy this room. This shows how a new guest can be accommodated in the hotel.




How to Cite

A. B. Jithendra. (2021). The Hilbert – Reimann Paradox. International Journal of Mathematics And Its Applications, 9(4), 121–126. Retrieved from



Research Article