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Welcome to /sci/. If you're here for homework help go to >>>/hwk/. If you're here for religion or politics, fuck off.

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Does 0^0 = 1?

Make your case, why or why not. If not, what should it be defined as?


b^a should be the number of functions from a set of size a to a set of size b. There is one function from the empty set to itself, namely the empty function. This shows that 0^0 should be 1.






actually 0^0 is not defined. It is often assumed 0^0 = 1 for specific theorems and statements to be shorter.


It's an indeterminate form, https://en.wikipedia.org/wiki/Indeterminate_form

Go here: http://fooplot.com/ and put in the following equations to see why.

We can all agree 1^x is 1 for all x. (put 1^x in as a function)

There are two forms of functions involving exponents: power functions (e.g. x^2) and the exponential functions (eg. 2^x)

Power functions:

As we reduce from powers greater than one to powers less than one, the shape of the curves change. Compare x^2 and x^(1/2). As we decrease the exponent, we get a "sharper" corner on the curve near x=0. Try it: x^(1/10) then x^(1/100) then x^(1/1000) and so on. That "sharp corner" appears to approach 1 as we decrease the exponent towards zero (x^0) but never quite reaches it until we increase the denominator to infinity (hence, an indeterminate form). If we imagine going all the way to infinity, then the curve would straight vertical from 0 to 1 at the origin, and then a 90-degree turn at y=1. So, 0^0 would equal every number between 0 and 1, which is silly.

Exponential functions:

As we reduce the base of the exponential function from bases greater than one to bases less than one, the shape of the curve reverses horizontally (compare 2^x and (1/2)^x). As we continue decreasing the base, we see that the function starts to get a "sharp corner" going towards the origin. Try it: (1/2)^x then (1/10)^x then (1/100)^x then (1/1000)^x and so on. If we imagine going all the way to infinity, then the curve would be a vertical line going from 0 to infinity at x=0, and then a 90-degree turn at the origin and the curve would be y=0 everywhere else. So 0^0 would equal every number between 0 and infinity, which disagrees with the first result we derived above, and is silly anyway.



Many people have defined 0^0 and the usual definition is 1 for various reasons. It is far from «not defined».


You would only call it an indeterminant form if you got 0^0 by taking some limit and plugging in 0. Even then, 0^0 has a well agreed-upon definition so you would just say that the exponential is not continuous at (0,0).

>We can all agree 1^x is 1 for all x. (put 1^x in as a function)

>Ad-hoc argument from limits of sequences of functions.

This is why it's wrong to attempt to teach kids calculus before they have a solid grasp on algebra. You get bizarre arguments that hinge on some analytic property holding in a case that it clearly does not when the whole context was about something elementary.

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Can we have a thread that discusses what exactly intelligence is and how it is measured? Most of the discussion I see here about intelligence is centered around group difference in IQ, and sometimes the heritability of IQ and the effects of IQ. But sometimes I have a feeling that many of the papers mean less to me when I don't have a good enough understanding of what exactly intelligence is in general. So I just want a thread discussing questions such as: (this is gonna be a long list by the way).

>what is intelligence? What is IQ? Is IQ the same as intelligence?

>what is the difference between intelligence and personality?

>What is g-factor, and how is it different from IQ and intelligence?

>what are the different theories of intelligence, and which ones are more accepted by academia?

>what is EQ and is it important? I see most people shit on EQ, but I still see a lot of papers mentioning EQ when I look for IQ on google scholar

>Where can I get a better understanding of psychometrics?

>What is the current state of research in IQ? Which subjects are they focusing on? Any new theories or old ideas being phased out? General consensus?

>How accurate are certain IQ tests? What external factors could influence test results?

>What the fuck is factor analysis? How is it calculated and what do the values mean?

>What is heritability and what is its significance?

I know that it does not mean that X% of your IQ comes from your genes when IQ is X% heritable, but rather that 50% of the variance in IQ in the general population comes from genetics. But I'm not sure about its significance since for one thing, the environment could change or be different in different parts of the world, thus having a different effect. How does epigenetics play into this? What's a more intuitive understanding of heritability of IQ?

Basically anything that helps people understand what they're looking at when reading and IQ study, things that give people a broader undPost too long. Click here to view the full text.


>what exactly intelligence is

There is no agreement on what intelligence actually is, it's just some vague psychological mysticism, like consciousness in the sense of the soul.


Wikipedia has an "outline of human intelligence" which I think might be a good place to start.


It's not well organized, and some of the things listed there aren't popular theories in academia. But to get some background information quickly it might work.

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I have n number of marbles and n ≤ 100. If I group the marbles into some groups of three, I will have

2 marbles left that belong to no group. If I group the marbles into groups of five, I have no marbles

left. But when I group them into groups of seven, I will have 4 marbles left. How many marbles that I

actually have? In other words, determine the value of n

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Too add to this if you know your 3 times table you know that 3 30s are 90 so that means that 31 is 93 which is 2 marbles less than 95 and if you know your 7 times table then it should be pretty easy to guess which number it is without even having to use a formula. Now that I think about maybe >>5003 is less complex than the way I did it.



It’s 95, took me two minutes and a pencil and paper.



>an obscure problem that only shows up in middle school math tests

The Chinese remainder theorem see a lot of use in adult math.



Seems like it might, but can you give examples?




The only thing I remember off the top of my head is RSA, but they'd probably explain it better than I would.

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I don't have a lot of patience for philosophy personally, but some may enjoy it.

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¿Does anyone here speak category theory?


Go to /tech/ and ask for a certain Mr.Haskell, they'll help you


http://paperkast.com/ - new link-aggregator exclusively for papers, thought /sci/ might be interested in this


Looks neat, although I don't really understand why they say at most two tags will be sufficient to categorize everything when every discipline is to have papers on there.

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Time to start this board again.

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Has the boot procedure succeeded, son?


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