Apr 14, 2016 · Considering this, it would make more linguistically and notationally valid sense to replace ‘ $=\mathtt{DNE}$ ’ with ‘ $\:\mathtt{DNE}$ ’ (omitting, or for typographic clarity instead substituting with a space or two, the ‘ $=$ ’).

Feb 5, 2022 · $\lim \limits_{x \to \infty} \sin{(2x)}$ = DNE. So, it went. $ 0 \cdot DNE$ Is this always the case, especially for transcendental functions like trigonometric functions? If $ 0 \cdot DNE$ can be equal to zero, then why is $ 0 \cdot \infty$ indeterminate?

$\begingroup$ I don't think DNE is unambiguously wrong, as there's no standard definition for what it means. In many calculus classes, a limit is said not to exist if there is no real limit, and positive/negative infinite limits are a subset of these. $\endgroup$

$\begingroup$ The question asks to show that the limit DNE. According to the rule you mentioned, it means that the denominator will reach $0$ faster than numerator, so that the equation DNE as $(x,y)\to(0,0)$? $\endgroup$ –

Nov 3, 2024 · DNE $\implies$ LEM $\implies$ DS $\iff$ efq; LEM + DS $\implies$ DNE; But then, this means that LEM $\iff$ DNE, without any "explicit" need of efq, which refutes a convincing negative stance that DNE requires LEM + efq, leading to obvious confusion. Question: I am not at all experienced in logic, and my proofs might be erroneous. Thus, if ...

Mar 1, 2016 · Prove f is continuous and that f'(0) DNE. Ask Question Asked 9 years, 1 month ago.

Jan 7, 2018 · Divergence means the limit doesn't exist. "Divergence to $\infty$" is a special case of divergence, and we sometimes say that the limit exists in those cases, but strictly speaking it doesn't (unless we're working in the extended reals, which as far as I can tell is mostly done just to indulge in this specific abuse of terminology (yes, I know there are legitimate reasons to use …

Sep 25, 2017 · Is there a proof not using $\\bot\\vdash\\varphi$, proving that Law of The Excluded Middle implies Double Negation Elimination in natural deduction? The ones I've seen would use $\\bot\\vdash\\varphi$ at...

Aug 18, 2015 · This webpage explains the difference between indeterminate and undefined operations in mathematics.

$\begingroup$ @Swivel But 0 does equal -0. Even under IEEE-754. The only reason IEEE-754 makes a distinction between +0 and -0 at all is because of underflow, and for +/- ∞, overflow.