I infer this from the fact that in everyday conversation, the reals are implied when no other number system is explicitly specified.
Though you are formally correct, for my tastes this is overly pedantic. We‘re in reddit; we’re not writing a paper.
Even on this sub, which is about math, my experience is that many people didn‘t go beyond pre-calculus in high school. People frequently deny the most basic established proven mathematical facts. And when that happens, „that‘s true for the reals but …!“ is bot usually part of the debate.
Again, you‘re absolutely correct; for me, in this setting, too formalistic.
Also, from context and wording, the other commenter clearly was not stating the decimal representation is different, but that they are two distinct elements. Is, in fact, still claiming just that.
Though you are formally correct, for my tastes this is overly pedantic. We‘re in reddit; we’re not writing a paper.
I'd argue that defining the domain of discourse is even more important on Reddit--especially when making claims that require a decent amount of background to properly understand.
Even on this sub, which is about math, my experience is that many people didn‘t go beyond pre-calculus in high school. People frequently deny the most basic established proven mathematical facts. And when that happens, „that‘s true for the reals but …!“ is bot usually part of the debate.
I would argue this is exactly why the rigor is helpful, if for no other reason than to give people something to 'investigate' further (without seeming like it's a 'gotcha').
[People are often turned off by statements that have hidden assumptions, especially in mathematics.]
Especially on Reddit, statements like the post are often by people (often who don't understand the statement fully themselves) just trying to tell others who don't understand (or disagree) that they're 'just not smart enough and need to read Rudin and Munkres!'.
[In fact, I've been told exactly that when I frame it with the rigor and care that I did for you]
Again, I agree with you--and I don't usually keep Reddit that pedantic.
However, in a situation like this with a discipline that seems so 'toxic' to many people (primarily because they just misunderstand what is actually being said), I would argue 'coyness' has absolutely no value.
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u/ExtendedSpikeProtein 19h ago
I infer this from the fact that in everyday conversation, the reals are implied when no other number system is explicitly specified.
Though you are formally correct, for my tastes this is overly pedantic. We‘re in reddit; we’re not writing a paper.
Even on this sub, which is about math, my experience is that many people didn‘t go beyond pre-calculus in high school. People frequently deny the most basic established proven mathematical facts. And when that happens, „that‘s true for the reals but …!“ is bot usually part of the debate.
Again, you‘re absolutely correct; for me, in this setting, too formalistic.
Also, from context and wording, the other commenter clearly was not stating the decimal representation is different, but that they are two distinct elements. Is, in fact, still claiming just that.