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This should be Gallium the metal that melts slightly above room temperature.

if it were to melt at room temp, the spoon would not be formed unless you happen to do the experiment of stir-dissolve in a cold storage.

It does not melt at room temperature but easily melts in your hands because of your body heat .

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@sackboy

 

holy crap man ! those numberphile videos are great.. nay awesome. Maths is seriously badass. Wonder why they dont use such concepts and teaching techniques in schools to entice students towards mathematics ? I mostly never liked maths, got sad marks all through out school except 12th where i studied like a man posessed with a clear mandate that this is the last time i would do anything with equations that had numbers and letters both. got really good marks in high 90%s but never thought of studying the subject further.

 

of late as i have been reading articles about maths' applied usage- 'how to make a perfect and well liked song (tunes, verse length, tempo and a generalised human reaction to them) using mathematical equations' and now this theoretical part of the subject in this video channel; and i can say that this is one subject that is the mother of them all.

 

:majesty:

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I am good at math that is not school sh*t , the concepts are clear to me but problem solving annoys me a lot . I somehow can't do it , the education system sucks . I love the concepts of mathematics and have even delved into some very deep concepts but the school stuff is too boring for me .

 

None the less Zenos paradox is one of the most interesting paradoxes , paradoxes related to infinity fry my brain , like this one

 

http://en.m.wikipedia.org/wiki/Galileo%27s_paradox

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For me the Monty Hall problem was pretty easy to figure out :|

 

Also what is about galilieo's pardox as maybe I'm don't get it or is it too simple

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Its very simple but its a paradox but you can never explain it .

 

Once you see the solution the Monty hall problem seems easy but if you were asked randomly then you wouldn't have understood it.

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Well I think that there is no paradox about galileo's paradox, but that is sure because I'm not understanding something

 

The monty problem is pretty easy but it took me some time to embrace it when I first got to know it, maybe that is why :|

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Man think about it for every number there is a square but for every number a square root does not exist , so in a set containing all numbers , there should be equal number of squares and normal numbers because every number has a square but that isn't true because many number don't have roots .... Did I make any sense ?

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Yes, because every number has a square, but every number also has a square root, not every one has a perfect square root(i.e. in integer or err rational)

 

So Numbers with squares > Numbers with integer square roots

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Yes, because every number has a square, but every number also has a square root, not every one has a perfect square root(i.e. in integer or err rational)

 

So Numbers with squares > Numbers with integer square roots

Now understand that in a set of all numbers , all numbers must have a square so

 

Number of ermmm numbers = number of squares

 

Whereas all numbers don't have roots

 

So number of roots > number of numbers

 

But every square has a root ... Try making a relation now :P

 

 

Its just one of the weird things about infinity.

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You can't compare infinity to itself.

 

Number of numbers =

Number of Squares =

 

You can't compare the two. It's like saying

 

∞ + 1 =

∞ + 2 =

=> ∞ + 1 = ∞ + 2

=> 1 = 2

 

The point at which you compare infinity to itself your equation becomes invalid.

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You can't compare infinity to itself.

 

Number of numbers =

Number of Squares =

 

You can't compare the two. It's like saying

 

∞ + 1 =

∞ + 2 =

=> ∞ + 1 = ∞ + 2

=> 1 = 2

 

The point at which you compare infinity to itself your equation becomes invalid.

I have seen the numberphile video on infinity too and I know this already , but its just a logical paradox already explained by the weird properties of infinity .

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haha yeah, that is the beauty of seperation of theory vs reality. not all theoratical hypothesis can or will be true, they just wont; but streaching the limits (not in mathematical sense) of our base by thinking up absurd paradoxes like so are the steps towards technological improvememts in real life.

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You don't make statements like these so simply: "number of roots > number of numbers". There is nothing wrong with an infinite set having the same "number" of elements as some of its proper subsets. When you are "counting" number of elements of an infinite set, you are actually calculating the so-called cardinality of that set. Think of how one counts the number of apples. We pick the first apple and mark 1 in our minds, then the second and so on. If there are n apples, we actually make a bijective map in our mind from the set of apples to the set {1, 2, ..., n}, and then say that there are n apples, because the set {1, 2, ..., n} has cardinality n. The actual study of cardinality requires a formal Set Theory course, which you may or may not do depending on what you'll study next. For starters, I can recommend reading the first chapter of Munkres' book "Topology". The first chapter deals with some basic set theory, and can be understood(albeit with a lot of effort) by a recent high-school pass-out.


 

And you CAN compare infinities. There are infinite number of infinite cardinal numbers. For example, the cardinality of the set of all real numbers(or even of all irrational numbers) is greater than that of all rational numbers or integers. So there are "more" irrational numbers than there are rational numbers. You people will need some reading to do before appreciating these things. Do look at Munkres, if you are interested enough.

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