Disproof of dirac delta function

Dirac's Delta function is a wrong theory and here is an informal disproof: First, let's draw a rectangle function: Assume a > 0. R(x) = 0, if |x| > a, = 1 / 2a, if |x| < a. Then R(x) is a rectangle whose bottom side is between -a and a on the x-axis. So the rectangle has the width of 2a. The R(x) rectangle's height is 1 / 2a. Thus, the area of the R(x) rectangle is: A(a) = 2a / 2a = 1. Now, let's find the limit when a becomes infinitesimally small. lim ( a -> 0, A(a) ) = 2a / 2a = 1. Now, the R(x) rectangle is becoming very thin and very tall, as the rectangle's width shrinks and its height elongates. But, the speed of horizontal shrinking and the speed of vertical elongation are identical. That is why the limit of the area still converges to one. Next, let us see the definition of Dirac's Delta function: D(x) = 0, if x != 0, = +INF, if x = 0; and D(x) must satisfy the following requirement: Integral( from -INF to +INF , D(x) ) = 1. Let's get the integration of D(x) from the first definition: Integral( from -INF to +INF , D(x) ) = 0 + ... + 0 + INF + 0 + ... + 0 = +INF != 1 Note that "1" is a constant, a fixed number. +INF is not a constant, not a fixed number, but a variable that perpetually increases at a certain speed. Thus, +INF cannot be equal to 1. Thus, there cannot exist such D(x). Q.E.D. The error that Mr. Paul Dirac committed is that he equalized infinitesimality with zero. Zero is a constant, a fixed number that does not change over time. In contrast, infinitesimality, such as 1 / INF , is a variable that decreases perpetually in its magnitude. The erroneous part of the definition of Dirac's Delta function is: D(x) = +INF, if x = 0. Mr. Paul Dirac used the variable INF and the constant 0 in the same equation and that was the error. This author argues that any mathematical theory based on Dirac's Delta function is a faulty one, because Dirac's Delta function is a mathematically wrong function. Not many mathematicians have the bravery to challenge the accuracy of a colossal, historic Nobel Laureate like Mr. Paul Dirac, because doing so might jeopardize their professional reputations. This is why the falsehood of Dirac's Delta function has persisted in mathematics for a century. It is time to correct the errors, ladies and gentlemen. This author also disproved Mr. Albert Einstein's special and general relativity theories, if you are interested: https://vixra.org/abs/2009.0211 https://vixra.org/abs/2010.0192 Thank you and enjoy //:-) --from Alaska