In this paper an attempt is made to include division by zero in ordinary arithmetic. Counting or measuring is done to get the value of multiples, powers, quotients, sums and differences of zeros. Zero divided by zero is taken to be equal to one. There are many infinities and many zeroes. The biggest of all infinities cannot be imagined and the smallest zero cannot be imagined also. An attempt is made to define a mathematical structure from the set of real numbers, zeros and infinities. Some fallacies have been resolved. Implications of allowing of division by zero on the quadratic equation when ð‘Ž = 0 and Newton's law of gravity and light deflection by gravity.
Keywords: division by zero, number, Hilbert hotel, zero, infinity, -0, negative zero, nothing, Euler number