Intereting Posts

A criterion for a group to be abelian
Does the order, lattice of subgroups, and lattice of factor groups, uniquely determine a group up to isomorphism?
Order of $\phi(g)$ divides the order of $g$
Is there any general formula for the sequence $S_n=\sum_{k=1}^n k^k$?
An entire function with periodic bounds
Intersection of Connected Sets
Prove that the projection $p_i$ from the product space $X_I S_i \tau$ into $S_i \tau_i$ is open for each $i \in I$
What is the dual space in the strong operator topology?
Let $f(z)$ be analytic on $\mathbb{D}$ = {${z\in\mathbb{C}:|z-1|<1}$} such that $f(1) = 1$, if $f(z) = f(z^2)$ for all $z\in\mathbb{D}$,
When does a continuous map $f:X\rightarrow \mathbb{H}P^n$ lift to $S^{4n+3}$?
Uniform Spaces: Completeness
Prove by induction that $10^n -1$ is divisible by 11 for every even natural number
Finding the inverse of the arc length function
subdifferential rule proof
Are all numbers real numbers?

Is it wrong to represent a dependent variable and a function using the same symbol? For example, can we write the parametric equations of a curve in xy-plane as $x=x(t)$, $y=y(t)$ where $t$ is the parameter?

Also, if someone write the following equation

$y=y(t) = t^2$

- Integral eigenvectors and eigenvalues
- How find the sum of the last two digits of $(x^{2})^{2013} + \frac{1}{(x^{2})^{2013}}$ for $x + \frac{1}{x} = 3$?
- How to prove $\lim_{x \to 2} x^2 = 4$ and make sure it's correct?
- Find the latus rectum of the Parabola
- How to solve $\mathrm{diag}(x) \; A \; x = \mathbf{1}$ for $x\in\mathbb{R}^n$ with $A\in\mathbb{R}^{n \times n}$?
- Algebraic proof that if $a>0$ then $1+a^9 \leq \frac{1}{a}+a^{10} $

where $y$ represents the dependent variable and t represents the independent variable, then is it wrong to say that $y(t)$ is merely used to represent the value of the dependent variable, $y$ when $t$ equal some value and $y$ in $y(t)$ does not represent a function?

- Pursuit curves solution
- Algorithm for computing square root of a perfect square integer?
- Integral ${\large\int}_0^1\left(-\frac{\operatorname{li} x}x\right)^adx$
- Determining the parameters for a spiral tangent to an arc and intersecting a specified point in 2D.
- Please help to complete proof of inclusion and exclusion principle
- Integral $\int_0^1\frac{\ln x}{x-1}\ln\left(1+\frac1{\ln^2x}\right)dx$
- A lemma about extension of function
- Can I disprove a claim using the contrapositive?
- Proving the AM-GM inequality for 2 numbers $\sqrt{xy}\le\frac{x+y}2$
- Proving the mean value inequality in higher dimensions for a differentiable function (rather than $C^1$)

The difference between $y$ and $y(t)$ is this: $y$ is a function and $y(t)$ is the value of the function at the point $t$. Often people write $y = y(t)$ which is supposed to emphasise that $y$ is a function of the variable $t$, but in absolute terms, the two things aren’t equal (even if $y$ is a constant function).

Another possible source of confusion is a statement of the form “consider the function $y(t) = t^2$”. As mentioned above, $y(t)$ is not a function. However, a function is determined entirely by its domain and its values at each point in the domain. Assuming we know the domain (which people often neglect to state), by specifying $y(t)$ as a formula in $t$, we know the value of the function at each point in its domain which determines the function $y$. So even though neither side of the equation $y(t) = t^2$ is a function, provided the domain is clear, it does uniquely determine a function.

- Finding values for integral $\iint_A \frac{dxdy}{|x|^p+|y|^q}$ converges
- Clarification on local global criteria
- Question about Quaternion group $Q_8$ and Dihedral group $D_8$
- Measure of set of rational numbers
- Geometrical interpretation of $I(X_1\cap X_2)\neq I(X_1)+I(X_2)$, $X_i$ algebraic sets in $\mathbb{A}^n$
- Compute the inverse Laplace transform of $e^{-\sqrt{z}}$
- Existence of a Riemannian metric inducing a given distance.
- Adjoint of an integral operator
- The free monoid functor is fully faithful?
- Extension of the Jacobi triple product identity
- Proof that a certain derivation is well defined
- How to find $\int_{0}^{1}\dfrac{\ln^2{x}\ln^2{(1-x)}}{2-x}dx$
- Are all Infinite Simplicial Complexes non-compact?
- Correspondence between Ext group and extensions (from Weibel's book)
- Roots of a polynomial