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Thread: Mathematics and precedence rules

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Re: Mathematics and precedence rules
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Re: Mathematics and precedence rules
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Re: Mathematics and precedence rules
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Re: Mathematics and precedence rules
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If 3/2 is a fraction then why isn't pi/2? Three is a constant, pi is a constant. Same thing, really. And anyway, if we figured out all the decimals of pi, we could very well turn it into proper fraction form, just with arbitrarily long numbers in the numerator and denominator.
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Re: Mathematics and precedence rules
You can't figure out all the numbers of pi. It's irrational.
So the only way you can have pi as a fraction is pi/1."I'm just going on motive and opportunity here and the fact that if the earth got swallowed by a black hole, I'd look suspiciously in your direction first."
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Re: Mathematics and precedence rules
Nope! 3/2 is a fraction (the actual term is a rational number) because 3 and 2 are integers. The fact that they're constants doesn't factor into it, p/q is also rational provided p and q are integers, even if they aren't constant. Integers are not arbitrarily long, either, since infinity is a limit, not a number.
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Re: Mathematics and precedence rules
Probably not, actually. Columbus was about four hundred years after Leif Ericson, who was the first European to make landfall in the Americas. But according to one of the sagas, Leif already knew about Vinland from a guy with the impossibly marvelous name of Bjarni Herjólfsson, who, along with his crew, had been blown off course there several years previously.
Of course other sources have it being Leif who was blown off course and wound up in Vinland, so who knows...As I've tried a thousand times
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Re: Mathematics and precedence rules
You can't figure out all the digits of pi because it never ends  it has infinitely many digits, and never starts repeating. There is no way to write pi as a fraction.

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Re: Mathematics and precedence rules
You have answered a different question.
This is never going to happen, π is irrational. The term irrational means that you can never write it down as a rational number. A rational number is one which can be written down as some P/Q where P and Q are integers. This has been proven, though IIRC the proof is a little subtle.p = 4
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well, rounding is only done in favor of less writing down (are you going to write every decimal? have fun with Pi) but that doesn't mean you can round off and calculate on with the rounded off numbers. You always continue with the non rounded numbers. I have been punished for not doing this in school (our teacher sometimes was slightly sadistic in making math tests like these). In maths acutally 2 things you need to know: 1) what is a function? (and how does it work and hwat can you do with it) 2)every numeral representation of a number is a range unless otherwise defined or reasoned.
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Re: Mathematics and precedence rules
Hurray, one explanation I don't have to do. Although the additional requirement that q≠0 needs to be added for the definition to be complete. Ie a rational number is defined as "p/q where p, q are integers and q≠0."
Now, for even/odd:
An even number is any integer that can be expressed as 2m, where m is any integer.
An odd number is any integer that can be expressed as 2m + 1, where m is any integer.
So, for the case of proving that odd + odd = even (To bastardize the language a bit), we have:
(2m + 1) + (2n + 1) = 2m + 2n + 2 = 2(m + n + 1) = 2k
The last "step" is unnecessary, but I figured it was better to play it safe and include it. It should be clear that k = m + n + 1 and we know k to be an integer because of the fact that integers are closed under addition.
Bit of a weak explanation, but meh.Last edited by Ashery; 20121028 at 04:08 PM.

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Yup. And anyone using the term 'dark ages' is instantly suspected to have little clue of the Middle Ages.
Lesson being: if you give some examples of basic facts you know, be sure everything you list is in fact accurate and not just a common misconception you picked up somewhere.Not a member of the Bayesian Conspiracy.Honestly.Probably.Maybe.
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Just to further beat this point into the ground: technically speaking, the line "who the US's first president was", is, on account of the wording, more accurately answered by 'John Hancock' than 'George Washington'*. The reason for this being that while Washington was the first person to hold the office of 'President of the United States of America', the US's first president (note lack of capital) would have been Hancock due to him being the president of the Continental Congress when independence was declared.
Pedantic? Yes, but it seemed fitting given the main topic of the thread
*There are other potential answers that can be argued for as well, but Hancock is probably the strongest option.

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Re: Mathematics and precedence rules
This, of course, doesn't actually matter: When they found America, there were already people living there. It had been discovered by them first, and while either Leif, Bjarni, or some other viking did make a legitimate discovery, they were by no means the first people to do so (had they been, they wouldn't have found people there, though there is technically a possibility for that to happen that simply didn't).
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That would depend on when the United States actually started to exist as an entity. Is the current United States under the Constitution the same as the country that existed under the Articles of Confederation or before? The Declaration of Independence mentions "the united States of America" (note lack of capital).

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Quite so. 4th of July 1776 is traditionally considered the date when the USA started officially existing as an entity, although you could also argue for 1783 (when Britain formally recognised its independence)  which would make the first president Thomas Mifflin. 1781 is a possibility, which would make the first president John Hanson.
Is the current United States under the Constitution the same as the country that existed under the Articles of Confederation or before? The Declaration of Independence mentions "the united States of America" (note lack of capital).
Basing a nation's age on a constitution however can be a bit awkward in any event, e.g. one could use it to make the argument that France has only existed since 1958. Things get very wonky in the cases of nations that don't have a written constitution, such as the UK*.
Regardless of what the most accurate answer actually, the existence of this discussion just goes to show that "who the US's first president was" cannot really be considered as basic a fact as ForzaFiori assumed it could
*it also leaves the proverbial door open to the 'type identity vs. token identity' discussion and how/whether that particular philosophical distinction does/should apply to countries.Last edited by Mr.Silver; 20121029 at 11:02 AM.

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Re: Mathematics and precedence rules
Well, I'd say that ambiguity is still better than just being plain wrong like about who discovered America or the Middle Ages being dark
Now I do wonder about the 'capital of Australia' bit; many, or even most, mistakenly believe it to be Sydney. Including me to be honest until I was corrected in, dunno, 8th grade maybe?
That said, the little excursion on who was the first president of the USA under what criteria was quite interesting. But given the presidents are numbered, shouldn't there be an 'official' answer to it or at least one endorsed by the government?Not a member of the Bayesian Conspiracy.Honestly.Probably.Maybe.
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Re: Mathematics and precedence rules
Only when defined for Euclidean geometry in a perfect plane. Since the universe is not perfectly Euclidean* due to pesky things like gravity, the actual value of pi  the ratio of circumference to diameter fluxuates depending on where you are. Somewhere, it's rational.
*Although apparently it seems to be basically Euclidean, which is too bad. I'd much rather live in a hyperbolic universe. I want my pentagon with five interior right angles.
A valid point, which is why I stipulated 'European.'
(Strangely, the Norse may well not have been the first people to discover Iceland. There's some evidence that Irish monks used it as a prayer retreat before the Norse colonization. However they were certainly the first to *settle* it, as one can hardly count a seasonal population of celibate men as any sort of colonization.)As I've tried a thousand times
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Re: Mathematics and precedence rules
Last edited by nedz; 20121029 at 09:23 PM.
p = 4
Consider a 5' radius blast: this affects 4 squares which have a circumference of 40' — Actually it's worse than that.
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Um... The Dark Ages are not The Middle Ages... Dark Ages is still a perfectly valid name for the Early Middle ages. Normally from the Fall of Rome to around 1050. It's really a much more defined period than the Middle ages.
Poor example. The date the UK came in to existence is very easy. 1 January 1801, the date the twin 1800 Acts of Union came in to force (and in 1922 in its current state).GnomeFighter, Membership Advisor, Henchpersons Union, South and Central (UK) branch  Ask about membership today!
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The Dark ages was so called because:
For Historians: there are very few written documents.
For the Church: Christianity retrenched as 'pagan' hordes swept through Europe.
Archaeologists don't like the term and it is considered outdated.
The term Migration period is generally preferred, which overlaps with the, so called, Age of Invasions in Britain (Romans to 1066).
The Dark ages were typically regarded as being from the end of the western Roman empire to the rise of the Carolingians. We now call that period late antiquity / early middle ages.p = 4
Consider a 5' radius blast: this affects 4 squares which have a circumference of 40' — Actually it's worse than that.
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The 'official' numbering scheme in the USA counts holders of the office 'President of the United States of America' (which are also easier to keep track of than the earlier 'presidents' because they have fixed terms). Unfortunately it doesn't actually provide the accurate figure for how many different people have held this position either, because it counts Grover Cleveland's two terms separately.
So yeah, just because it's 'official' doesn't mean it's technically correct
Funnily enough there is a similar 'official' numbering discrepancy in the British monarchy. Because monarchs only started being numbered after the Norman conquest, King Edward I was actually the second monarch to be called Edward (Edward the Confessor having been the first) and so on with all subsequent Edwards.
Yes, in much the same way that the USA is considered to have come into existence on the 4th of July 1776 with the Declaration of Independence.

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Re: Mathematics and precedence rules
p = 4
Consider a 5' radius blast: this affects 4 squares which have a circumference of 40' — Actually it's worse than that.
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