It seems like the Dirac Delta function is discontinuous as it has a value of $\infty$ at $x=0$ and $0$ everywhere else. It looks to be same as the Kronecker Delta Function, which we know to be discrete.
2026-03-25 11:10:53.1774437053
Why is a Dirac Delta function called continuous when it's seems to be discrete?
4.7k Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in PROBABILITY-DISTRIBUTIONS
- Given is $2$ dimensional random variable $(X,Y)$ with table. Determine the correlation between $X$ and $Y$
- Statistics based on empirical distribution
- Given $U,V \sim R(0,1)$. Determine covariance between $X = UV$ and $V$
- Comparing Exponentials of different rates
- Linear transform of jointly distributed exponential random variables, how to identify domain?
- Closed form of integration
- Given $X$ Poisson, and $f_{Y}(y\mid X = x)$, find $\mathbb{E}[X\mid Y]$
- weak limit similiar to central limit theorem
- Probability question: two doors, select the correct door to win money, find expected earning
- Calculating $\text{Pr}(X_1<X_2)$
Related Questions in CONTINUITY
- Continuity, preimage of an open set of $\mathbb R^2$
- Define in which points function is continuous
- Continuity of composite functions.
- How are these definitions of continuous relations equivalent?
- Show that f(x) = 2a + 3b is continuous where a and b are constants
- continuous surjective function from $n$-sphere to unit interval
- Two Applications of Schwarz Inequality
- Show that $f$ with $f(\overline{x})=0$ is continuous for every $\overline{x}\in[0,1]$.
- Prove $f(x,y)$ is continuous or not continuous.
- proving continuity claims
Related Questions in DIRAC-DELTA
- What is the result of $x(at) * δ(t-k)$
- Solution to ODE with Dirac Delta satisfies ODE
- How is $\int_{-T_0/2}^{+T_0/2} \delta(t) \cos(n\omega_0 t)dt=1$ and $\int_{-T_0/2}^{+T_0/2} \delta(t) \sin(n\omega_0 t)=0$?
- Approximating derivative of Dirac delta function using mollifiers
- How to prove this Dirac delta limit representation is correct?
- $\int_{-\epsilon}^\epsilon\delta(f(x))g(x)dx=\frac{g(0)}{f'(0)}$?
- Properties about Dirac Delta derivative
- Dirac / Fourier relation
- Prove that $\frac{1}{\epsilon}\int_{\mathbb{R}}f(t).\exp\left(\frac{-\pi(x-t)^2}{\epsilon^2}\right)dt \xrightarrow{\epsilon \to 0}f(x) $
- Integral involving delta functions and vector quantities
Related Questions in KRONECKER-DELTA
- Simplifying Product of Kronecker Delta Functions
- Looking for ${f_n}$ such that $\int_0^1 (x-t)^{m-1}f_n(t) dt = \delta_{n,m}$
- How to proof that a dual basis applied to the basis give the Kronecker delta?
- How is the dot product of two cartesian unit vectors equal to the Kroencker delta?
- Trouble with delta kronecker
- Equation containing cofactor of derivative and Kronecker-delta
- Do these integrals evaluate to terms involving Kronecker Deltas?
- Quantum Mechanics - Orthonormal Basis integration and Kronecker delta
- Does changing the order of the indices of the Kronecker delta within a summation matter?
- Kronecker Delta with 3 indices
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
I think it has to do with the fact that continuity is implied by differentiability and integrability, and since the Dirac-Delta function is differentiable and integrable, it is continuous.