Can a judge make it case law that 2×2=5?

Question

The following quote from Malcolm Turnbull is actually not what this question is about, but nevertheless it is a good-fit epigraph:

The laws of mathematics are very commendable, but the only law that applies in Australia is the law of Australia.

---

Though the scenario I give in this question is exaggerated, hypothetical, edge-case one, it is technically valid and showcases the essence of the question.

A recent question/answer seems to be telling us that it is perfectly fine for a judge to reject an argument even implicitly — i.e. without actually discussing it. Such a judgment might only be vulnerable to appeal, but in no way to judicial discipline / misconduct investigation. If not successfully appealed, it becomes case law — binding on all inferior courts. Where rights of appeal do not exist (e.g. the court is the top court in its jurisdiction), the judgment becomes set-in-stone law — until cancelled either by the same court or via legislation.

So, let's consider the same example as in that question, but more specific one:

Bob contends:

I am right and Rob is wrong because blablabla... 2×2=4 ...blablabla.

Rob defends:

No Bob is wrong, because blablabla... and 2×2 actually equals 5.

Bob replies:

But look, lets see what 2×2 equals to [math proof follows]. It is 4, you see.

The judge says:

I accept Rob's contention that Bob is wrong because 2×2=5. Bob has no case.

So, the judge implicitly rejects the math proof that 2×2=4 (as their Honour "does not have to address every argument raised in their judgement") and, effectively, makes it case law that 2×2=5.

Is this scenario technically/legally possible? Would the case law that 2×2=5 stand for some time? Will the judge not face any disciplinary consequences but just public outcry and reputation damages?

I appreciate that one might want to say that no judge would accept such an extremely outrageous merit-lacking argument as "2×2=5" and I totally agree (with hope). But the way this question applies to reality is that there is no clear boundary between "2×2=5" and any mundane argument that Rob might argue — as far as its acceptance by a judge is concerned.

Answer 1

Appellate judges make holdings on matters of law, and generally defer to the fact-finder in a given case (the jury, or sometimes the judge) on factual matters relevant to a case. So in a case that involved certain mathematical arguments, they would generally leave it to the jury to decide whether those arguments were reliable. Put simply, Appeals courts don't make binding decisions on issues of fact, only issues of law.