@AsDaGo said in #30:
> Damn, if you think 9.8*10^-17 is "greater than a few," I'm curious to know exactly how small you think "a few" is. (Also the word "few" only really makes sense when we're talking about integers.)
>
> Also, by the way, we shouldn't use subtraction to compare numbers, but rather division. So (15512081662300000022691067351/231523606900000000000000000)/67 = 15512081662300000022691067351/15512081662300000000000000000, and then we can 1 from that to get 22691067351/15512081662300000000000000000, which is approximately 1.5*10^-18, so the answer is approximately 1.5*10^-16 percent greater than 67.
Definition of "few":
a small number of:
"may I ask a few questions?"
Typically, 'small' means single-digit numbers, or ones from 10-20.
Yet, I am not the average person. Few, to me, means 0, yes literally 0. Therefore, "close" is an inaccurate word. You should use whatever 67 - 66.99... is. I could say "few" is -1 infact.
@chesspanda6 said in #31:
> Yet, I am not the average person. Few, to me, means 0, yes literally 0.
Wow, that is extremely different than the way most people use it. It's good to be different, but why would you use a word to mean something completely different than what most people use it to mean? It makes communication very difficult, and we also already have a word for 0 (namely, "zero").
> I could say "few" is -1 infact.
That contradicts what you said previously, so maybe you meant to say that you use it to mean less than or equal to zero? Either way, I've certainly never heard anyone use "few" to mean that. It's like if I decided to use the word "octopus" to mean "helicopter." It would make communication very difficult. "Have you ever flown in an octopus?" "...What?"
> Therefore, "close" is an inaccurate word.
You must have a very different definition of "close" than most people as well, or you don't understand scientific notation. Most people would consider two numbers that are within 1.5*10^-16 percent of each other to be very close to each other. Sure, the concept of "closeness" depends on context, but I can't think of a context in which those numbers wouldn't be considered close to each other by any reasonable person.
In case you don't understand scientific notation, 1.5*10^-16 percent is 0.00000000000000015%.
> You should use whatever 67 - 66.99... is.
I'm not sure where you got 66.99 from. The answer is 15512081662300000022691067351/231523606900000000000000000, which as I mentioned, is approximately 67.0000000000000001. In any case, as I also mentioned, you shouldn't use subtraction to compare numbers but rather division. But if you really want the result of the subtraction, please see #21.
@AsDaGo said in #32:
> Wow, that is extremely different than the way most people use it. It's good to be different, but why would you use a word to mean something completely different than what most people use it to mean? It makes communication very difficult, and we also already have a word for 0 (namely, "zero").
>
>
>
> That contradicts what you said previously, so maybe you meant to say that you use it to mean less than or equal to zero? Either way, I've certainly never heard anyone use "few" to mean that. It's like if I decided to use the word "octopus" to mean "helicopter." It would make communication very difficult. "Have you ever flown in an octopus?" "...What?"
>
>
>
> You must have a very different definition of "close" than most people as well, or you don't understand scientific notation. Most people would consider two numbers that are within 1.5*10^-16 percent of each other to be very close to each other. Sure, the concept of "closeness" depends on context, but I can't think of a context in which those numbers wouldn't be considered close to each other by any reasonable person.
>
> In case you don't understand scientific notation, 1.5*10^-16 percent is 0.00000000000000015%.
>
>
>
> I'm not sure where you got 66.99 from. The answer is 15512081662300000022691067351/231523606900000000000000000, which as I mentioned, is approximately 67.0000000000000001. In any case, as I also mentioned, you shouldn't use subtraction to compare numbers but rather division. But if you really want the result of the subtraction, please see #21.
1) Then, why do people say "few" instead of difference of 1, 2, or 3 (one, two, or three). In your view, saying "few", which is a commonly used word, as completely irrelevant.
2) That contradicts what you said above. If I said to someone, that these two numbers had a difference of a "few" (something like 500), they would just stare at me, and say "What?". The perception of a "few" is very vague, same with "close". Therefore, it's better to write the exact answer, or atleast an approximation.
3) Yes, I do understand scientific notation. Close, is yet again, very vague. Being not the average person, my perception of close is 0.0%. If, let's say, my range was more wider, I could say 500000 is close to 1, making "close" mean anything based on the person. It doesn't have a set meaning. Sure, others define close as something else, but the word never has it's limits.
4) Yes, sorry same thing, I am too lazy to look back lol. Yet again, my perception of "close" is 0, or a number extremely close to 0 (e.g. 10^-101)
@chesspanda6 said in #33:
> In your view, saying "few", which is a commonly used word, as completely irrelevant.
That's why I didn't use that word. You did.
> Yet again, my perception of "close" is 0, or a number extremely close to 0 (e.g. 10^-101)
That definition is circular, and I assume you're still using subtraction, not division (or you would say close to 1). Anyway, it seems that the misunderstanding was due to your unusual use of common words, so I guess I have nothing more to say on the matter except that you should consider trying to use words the same way everyone else uses them. Words are made for communication, and as we have just seen here, they cannot serve that purpose if two people have completely different ideas of what the same word means. Sometimes this happens because someone doesn't know the meaning of a word, but in this case you're doing it on purpose for some reason.
I guess you're trying to be extremely precise to be pretentious or something, but your own writing is riddled with self contradictions and imprecise language.
@AsDaGo said in #35:
> That's why I didn't use that word. You did.
>
>
>
> That definition is circular, and I assume you're still using subtraction, not division (or you would say close to 1). Anyway, it seems that the misunderstanding was due to your unusual use of common words, so I guess I have nothing more to say on the matter except that you should consider trying to use words the same way everyone else uses them. Words are made for communication, and as we have just seen here, they cannot serve that purpose if two people have completely different ideas of what the same word means. Sometimes this happens because someone doesn't know the meaning of a word, but in this case you're doing it on purpose for some reason.
>
> I guess you're trying to be extremely precise to be pretentious or something, but your own writing is riddled with self contradictions and imprecise language.
1) I mentioned both “few” and “close” because you were arguing about both. They’re not interchangeable, but they share the same issue: they’re vague terms. In mathematics (and other fields requiring precision), vagueness is exactly what we’re trying to avoid.
2) Dictionaries don’t give explicit definitions for words like these, because in everyday language they’re meant to be flexible. But in mathematics and science, precision is essential. Telling a scientist to add “a little” solution is meaningless if a 1% difference can determine whether the experiment works or fails. The same applies here: “few” or “close” don’t give us exact boundaries, and that’s why they are unsuitable in these contexts.
That’s why people in math use precise definitions and exact quantities, not because they are trying to be 'pretentious', but because vague words don’t work in this context. Mathematics is a place where exact measurements matter, so it makes sense to hold language to the same standard.
@chesspanda6 said in #36:
> I mentioned both “few” and “close” because you were arguing about both. They’re not interchangeable, but they share the same issue: they’re vague terms.
You were the only one to use "few." I even said you shouldn't use it because it only makes sense with integers (only whole numbers, really).
> In mathematics (and other fields requiring precision), vagueness is exactly what we’re trying to avoid.
I agree, which is why I did give the exact number if you look carefully. Ironically, you have failed spectacularly in doing the very thing you claim to be attempting (i.e., avoiding vagueness).
Anyway, it seems we have cleared up this completely unnecessary misunderstanding, so there's no need to continue the discussion.
@AsDaGo said in #9:
> Not quite. It's very close, but the answer is actually 15512081662300000022691067351/231523606900000000000000000 which cannot be represented exactly as a decimal.
??
But that long digit you typed 155.../231... is still EXACTLY 67, and can be represented EXACTLY as a decimal: 67.0
@IAHMCOL said in #38:
> But that long digit you typed 155.../231... is still EXACTLY 67
It's not. Rounding to 100 digits, it is
67.00000000000000009800757536055818936880945767608460664492178831894312544938155073291578026119633678
(but even that is not exact of course).
@LeChuchel said in #1:
> Can You guess the right answer of this math problem:
>
> 5565×55656655÷55565665656+62−0,57411274423480821=?
uhhhhh
idk i too lazy to lol
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