# Equations with No Solution **URL:** \ **Category:** Factual Questions\ **Tags:** science-math\ **Created:** [June 8, 2025, 3:14pm UTC](https://boards.straightdope.com/t/equations-with-no-solution/1019330 "2025-06-08T15:14:26Z")\ **Posts on this page:** 4\ **Page:** 7
**Author:** ![LSLGuy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lslguy/32/5813_2.png) [@LSLGuy](https://boards.straightdope.com/u/LSLGuy)\ **Post date:** [June 12, 2025, 3:41pm UTC](https://boards.straightdope.com/t/equations-with-no-solution/1019330/121 "2025-06-12T15:41:46Z")
But what he said was closer to > I don’t dispute that [formula] has no solution. … But what in my set of math axioms makes that so? I know the answer to the formula. I don’t know how/why I know. > > Please explain _that_ to me simply." It’s the meta question that’s interesting, not the brute algebra. ---
**Author:** ![The\_Other\_Waldo\_Pepper](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/the_other_waldo_pepper/32/12370_2.png) [@The\_Other\_Waldo\_Pepper](https://boards.straightdope.com/u/The_Other_Waldo_Pepper)\ **Post date:** [June 12, 2025, 3:50pm UTC](https://boards.straightdope.com/t/equations-with-no-solution/1019330/122 "2025-06-12T15:50:18Z")
> [@LSLGuy](#): > > But what he said was closer to “I don’t dispute that [formula] has no solution. … But what in my set of math axioms makes that so? I know the answer to the formula. I don’t know how/why I know. Please explain _that_ to me simply.” But the other thing he said in the OP — the thing we’d maybe need to explain to someone else, but which he’s already spelled out — is that: “If we are asked to solve the equation for x we end up with the equation 0 = 5 which is false.” So he doesn’t merely tell us that he doesn’t dispute that it has no solution; he tells us that 0=5 is false, and he tells us that solving this would mean ending up with the conclusion that 0=5; _that’s_ why he says he doesn’t dispute it. When is it okay for me to (a) be at a loss for words because I (b) note that those are already all of my words? ---
**Author:** ![Ynnad](https://avatars.discourse-cdn.com/v4/letter/y/4491bb/32.png) [@Ynnad](https://boards.straightdope.com/u/Ynnad)\ **Post date:** [June 12, 2025, 9:19pm UTC](https://boards.straightdope.com/t/equations-with-no-solution/1019330/123 "2025-06-12T21:19:54Z")
I suppose my motives for the OP might have been a little cryptic. I actually do know the basics of Proof by Contradiction, Axioms of the Real Numbers, The Law of the Excluded Middle, what an equal sign means, etc. I didn’t really need an explanation for me. By including “explain this to me like I’m five years old” I was hoping to get some ideas on how to better explain this to others who have very little experience with math but need to learn this for work. Nonetheless it was fun reading all of the responses. Thank you. ---
**Author:** ![LSLGuy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lslguy/32/5813_2.png) [@LSLGuy](https://boards.straightdope.com/u/LSLGuy)\ **Post date:** [June 13, 2025, 11:53am UTC](https://boards.straightdope.com/t/equations-with-no-solution/1019330/124 "2025-06-13T11:53:45Z")
While looking for something else I stumbled on this old thread that might be tangentially useful to the OP. > [@Any exceptions to either it's "A" or "not A"?](https://boards.straightdope.com/t/any-exceptions-to-either-its-a-or-not-a/636100): > > I’ve been told my thinking is more “black and white” than normal… I based some of my reasoning on a principle of logic that says that things are either “A” or “not A”. (I forget the exact details) I wonder if there are any exceptions…? Maybe quantum physics or the world of human emotions? I suspect that I would think that many of those so-called exceptions are just not thought about in the right way… [Previous page](https://boards.straightdope.com/t/equations-with-no-solution/1019330.md?page=6)