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Hey Affinity, i need your help with one more thing before i leave this place. I joined this forum for one main reason really, to find out what is going on here after browsing through a 3unit thread by someone asking to do some probability questions. This was one of the questions and the...

True that. Definitions are there to make math work and not hard. Appreciating definitions is another matter, but i get what you mean. the answer to the question: integrate {-1 to 1} 1/x^2 dx = 2 x infinity = infinity

A Field F is any set of objects with two operations (+) and (x) (usually called "addition" and "multiplication") defined in it, provided that these objects and operations satisfy the six Axioms of addition and multiplication. 2 is defined as 1+1. :p

Ok ok, so nike33's reasoning is wrong? can you confirm that absolutely? Because apparently he got the right answer which is quoted by the original question poser. And one more thing which is not really important but just that you know the question did ask for "combination" which means it...

I'm not sure what you mean by definitions come naturally. Surely you cannot not know any of the definitions without learning it first. If definitions did come naturally then math as a "subject" would not exist.

Thats fun. I like it. Though im still in dark on how to connect the formal definition with an intuitive idea of a limit. Maybe i should research the history of the definition.

Re: Re: how are these possible How original... thats what i call creativity.

Someone's got to help me out, i'm having nightmares about combinatorics. Who would've thought high school combinatoric questions could be this tricky. I don't like spamming so please help. HOW DO YOU GET 60480 WAYS :confused:

Always look at the fully worked solutions before attempting any question that you can't do. You don't learn from getting a question wrong or making a mistake (thats a misconception), but you learn from looking at the right solutions and memorizing every step of it by heart. Sooner or later...

Bush, the question says combination of 3-letter words. So according to the question all the arrangements you listed are indistinguishable. If i did count the permutations, ie different words that can be made, it came out to be something like 291 (i can't remember it now). But even that is no...

(l/-n)x + (m/-n)y = 1 equation of a tangent: xx₁/a² + yy₁/b² = 1 therefore if the line touches, it is at least a tangent to the ellipse, (l/-n) = x₁/a², and (m/-n) = y₁/b². now substitute l and m...

So no one is willing to help me?

I get your intuition of close enough would guarentee an existence, but what i don't understand is the formal definition which states: The limit of f(x) as x approaches c is L Lim {x->c} f(x) = L if and only if, for each e > 0, there exists a d > 0 such that 0 < |x - a| < d, then...

Yep i got ya. thanks. Someone explain the first part of my question please

How much time do mathematicians spend on memorizing axioms, definitions, theorems, lemmas ect... ? Do they spend more time on learning the precise definition of a theory than doing computations and learning algorithms? I'm curious to know...

Ok, can someone explain to me how this definition guarantees the existence of the limit or what is the point of the definition. After many attempts to understand it, im still as confused as ever. :mad:

I know the first way (the ordered way) is correct, but why? Can someone explain this to me please. And can someone derive for me or explain to me with logics the formula: ^(n+r-1)C_r for unordered selection with replacement.

i do not get this at all. how come i got 42 ways for my answer? # 3A's = 1 # 2A's = 6C1 # 1A's = 6C2 # 0A's = 6C3 # total ways = 1 + 6C1 + 6C2 + 6C3 = 42 what's wrong with my logics? did i not interpret the question right? fuck i'm stupid.