Prove or disprove the statement: For all real numbers $x,y$, $⌊xy⌋=⌊x⌋⌈y⌉$. What's wrong with my counter example?

Question

Prove or disprove the statement: For all real numbers $x,y$, $⌊xy⌋=⌊x⌋⌈y⌉$.

I used the counter example $x = 1.9$, $y = 1.9$.

$⌊1.9 \cdot 1.9⌋ = 3$

$⌊1.9⌋⌈1.9⌉ = (1)(2) = 2$

But the professor said that this statement was actually true and I got 0 marks. Does anyone know what was wrong with my counter example?

"4. 0/3. The statement is true, and can be proved." This was from an online course, I just wanted to verify before I said something and looked stupid. — Xero, Jul 27 '20 at 22:38
That statement does not provide an answer to the question. You have provided a valid counterexample and hence shown it cannot be proved. — Peter Foreman, Jul 27 '20 at 22:39
It's possible that instead of the ceiling of y he meant the floor of y. Everything looks right on my end so I'm going to send him an email. — Xero, Jul 27 '20 at 22:42
It still wouldn't be true. The same counterexample would give$$3=1\cdot1$$ — Peter Foreman, Jul 27 '20 at 22:43
It's exactly the question in the title with no typos. Prove or disprove the following statement: “For all real numbers x,y, ⌊xy⌋=⌊x⌋⌈y⌉.” (3 marks). — Xero, Jul 27 '20 at 22:45
If negative numbers are alowed then $-1/2, 2$ is an example.. The LHS is $-1$ and the RHS is $-2$. — markvs, Jul 28 '20 at 01:53
I’m voting to close this question because the professor is wrong and the question is meaningless. — user21820, Jul 30 '20 at 16:10

score 4 · Answer 1 · answered Jul 27 '20 at 22:37

The professor is clearly wrong unless the notation means something other than the floor/ceiling function or you misread the question. Double check to make sure the problem on the assignment matches what you just wrote here; then, go to office hours and ask the prof to take a look.

score 3 · Answer 2 · answered Jul 27 '20 at 22:35

3

Your example is true. There is nothing wrong with it.

answered Jul 27 '20 at 22:35

markvs

19,653

Prove or disprove the statement: For all real numbers $x,y$, $⌊xy⌋=⌊x⌋⌈y⌉$. What's wrong with my counter example?

2 Answers2