Shoutbox

I dont know the name in english so ill explain it.

Its when you have an equation and you have to prove its true for every n. for n=positive interger.

so u put in the equation n+1 and then u prove it that way...


So what is this type of math called??

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Its like geometry on a graph (x,y).... Also dont know the name.

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Originally posted by .Roy
Its when you have an equation and you have to prove its true for every n. for n=positive interger.

so u put in the equation n+1 and then u prove it that way...

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Induction.

Also what do you call it in calculus when you make something from
f( x ) to f( x ) '

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Originally posted by .Roy
Also what do you call it in calculus when you make something from
f( x ) to f( x ) '

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quote:

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derived function - the result of mathematical differentiation; the instantaneous change of one quantity relative to another; df(x)/dx

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quote:

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Originally posted by .Roy
f( x ) to f( x )

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We just call Function of X or... F of X for short... (derived function is probably the mathematical term for it though.

... okay... so I didn't see the '  lol...

quote:

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Originally posted by .Roy
I dont know the name in english so ill explain it.

Its when you have an equation and you have to prove its true for every n. for n=positive interger.

so u put in the equation n+1 and then u prove it that way...


So what is this type of math called??

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I dunno what it is called in English... Though I fail to see how putting n+1 in the equation would proof such an equation....

You just need to solve the equation in such a way that n is on the left of the equation and something else is on the right of the equation, where the equation is actually a "greater than" sign...

eg: solve it so you come to something like "n > 0".
eg: is n*8 > n always true if n=postive integer? yes, proof:
1) n*8 > n
2) (n*8)-n > n-n
3) n*7 > 0
4) n*7/7 > 0/7
5) n > 0

if that is what you meant

quote:

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Originally posted by UTI

quote:

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Originally posted by .Roy
f( x ) to f( x )'

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We just call Function of X or... F of X for short... (derived function is probably the mathematical term for it though.

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function of X is correct for f(x)... but note the ' after f(x), which means f(x)' is the derived function of x.

The ' wasn't a typo in his post...

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Originally posted by CookieRevised
function of X is correct for f(x)... but note the ' after f(x), which means f(x)' is the derived function of x.

The ' wasn't a typo in his post...

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I didnt describe what i meant enough...

John anderton got it though .

I mean to prove for example an equation is true, you first "say its true" and then prove its true for n+1. And then you find a way to insert the true statement in the new equation and u get something that is true for example n^2>0 and u know n^2 is always positive so...

didnt f(x )' mean everything out of x?

Voldemort, what you mean is compliment, it is used in set theory and related chapters like probabilty and stuff. it is also denoted by x^c or x bar. but in calculus, ' means derived function of the given function.
answer to first query : Mathematical Induction
answer to second query: Differentiation.

Cookie: In Dutch it's called "inductie" (used Wikipedia to get it).
It's a special kind of math, so I suggest you don't start doubting

Example:
Show that 1+2+3+...+n = (n(n+1))/2 is true when n is a positive integer.

You would solve that this way:
1. n=1, both sides equal 1, so it's true.
2. Assume that it is true for n=k, so if it is true for k+1 we have prooven it's always true.
3. We prooved that 1+2+3+...+k is (k(k+1))/2 is the first step, so we can replace the set of numbers with that expression. We get
(k(k+1))/2 + (k+1) = ((k+1)(k+2))/2
Then you solve the right and left side separately, in this both are
(1/2)k^2 +  (3/2)k + 1
We have now prooven it's true using induction