0

So here's my reasoning:

For any $x$, $y=0x+y$ will simply yield $y$, which would lead me to believe that $y=y$ would produce a horizontal line at, well, $y$... except, since for any $y$ the horizontal line will take at place at said $y$, I'd figure $y=y$ would produce an infinite set of horizontal lines stacked on top of each other.

Hence, all (x, y) pairs are valid solutions to $y=y$. I would assume this also extends to $x=x$ too if it is true.

Now, it is undeniable that both $y=y$ and $x=x$ are true statements, but everyone whom I asked this question either replied with saying this would produce nothing, or simply does not make sense to ask. Desmos seems to agree with the nothing result too.

What am I missing? Why would asking to plot $y=y$ be invalid if $y=c$ where $c$ is some constant or $y=x$ is valid? And if I am right, how could I prove it to those who disagree?

Iwaslazkis
  • 3
  • 2
    It may help to distinguish between the graph of a function of one variable (and if so, identify what function you have in mind), versus e.g. a more general subset of the plane (i.e., a set of the form ${(x,y) \in \mathbb{R}^2: \dots}$ perhaps defined by a list of one or more equations in $x$ and $y$ appearing in the $\dots$). The set of all $(x,y)$ for which $y = y$ is the entire plane and not the graph of a function of one variable. – leslie townes Mar 11 '21 at 01:03
  • 1
    Why not just make that long paragraph an answer – Kenny Lau Mar 11 '21 at 01:03
  • If someone asked me to graph the equation $y = y$, I'd say the graph is the entire $x-y$ plane. – littleO Mar 11 '21 at 01:12

1 Answers1

2

Desmos needs to find how many variables you're using, ie which is $x$ and which is $y$. It does this implicitly, but when you put an equation $y = y$ it evaluates that as $y-y = 0$, ie just a constant. Try putting any constant in Desmos with no variables and you'll see that it will not graph anything.

For $y = y$, there are infinite solutions. In the x,y plane, $x$ is not restricted so it can be any value. So yes, it is the whole x,y plane.

However this equation doesn't really convey any information. The 'solution' is trivial, so plotting it is unnecessary.

spectralblue
  • 301
  • 1
  • 6