- #1

does this equate all numbers or am i gettin this mixed up.

well that is not want i intend sending,find the derivative of 3^3^3^3^3^3....................^x,and then tell me what the integral of 0 really is.I rest my case

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- Thread starter mathelord
- Start date

- #1

does this equate all numbers or am i gettin this mixed up.

well that is not want i intend sending,find the derivative of 3^3^3^3^3^3....................^x,and then tell me what the integral of 0 really is.I rest my case

- #2

You're not making sense. The antiderivative of 0 is C, that is because information is lost when deriving. The derivative of any constant is 0. Where does "1=2=3=4" come from?

What's the difference between "a constant" and "any constant"?

Also, the definate integral of 0 on any interval is 0.

What's the difference between "a constant" and "any constant"?

Also, the definate integral of 0 on any interval is 0.

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- #3

Cyrus

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- #4

Alkatran

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'MANY TO ONE' FUNCTIONS DO NOT SHOW THAT 1 = 0. 'ONE TO MANY' FUNCTIONS DO NOT SHOW THAT 1 = 0. 1 DOES NOT EQUAL 0.

- #5

HallsofIvy

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I think I saw one of those on I95!

- #6

mathwonk

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- #7

SteveRives

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mathwonk said:

Yes! Exactly! And with this we are free to muse about the integral on its own terms -- it is its own thing. Which allosws us to ask the question: what is zero growing into as we add zero to it?

Such a question is a geometric-like way of thinking of the integral. And, as such, no one needs to think about antiderivatives to realize that such a thing is "definitely just zero."

- #8

Cyrus

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What ever happened to the constant of integration?

- #9

Cyrus

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I cant read your text because its not long enough rach, sorry. I always thought evaluating the integral was to do the antiderivative to it. Could you explain the difference please.

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- #10

quasar987

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The integral evaluated from a to b is 0, but the improper integral, i.e. the anti-derivative, is C.

- #11

- #12

- #13

quasar987

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- #14

MalleusScientiarum said:

Hey, I was just trying to make things easier to understand. If you're looking for the most general result, then might as well point out that a zero function (real or complex) has Lebesgue integral zero over

- #15

Cyrus

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- #16

so what does the derivative of the function 3^3^3^3^3^3^3^3^...........................^x gives us

- #17

[tex]\frac{d}{dx} 3^x = 3^x\ln 3[/tex]

[tex]\frac{d}{dx} 3^{3^x} = 3^x \ln 3 * 3^{3^x} \ln 3[/tex]

You can do the rest. However, I don't see how this has anything to do with the integral of zero or how 1=2=3=4.

[tex]\frac{d}{dx} 3^{3^x} = 3^x \ln 3 * 3^{3^x} \ln 3[/tex]

You can do the rest. However, I don't see how this has anything to do with the integral of zero or how 1=2=3=4.

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- #18

hypermorphism

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Let the function [itex]T(a) = 3^a[/itex]. The derivative of this function with respect to a is [itex]3^a \ln(3)[/itex]. Thus you have the function T(T(...(T(x))...)) where T is composed n times with itself. Let [itex]3_i(x)[/itex] be the power tower of 3 to order i where the ith position is replaced with the variable x, and [itex]3_i[/itex] be the power tower of order i. The derivative of the given function is then [tex]\frac{d}{dx}T(T(...(T(x))...)) = T'(T(...(T(x))...))*T'(...(T(x))...)*...*T'(x)[/tex]mathelord said:so what does the derivative of the function 3^3^3^3^3^3^3^3^...........................^x gives us

[tex] = \prod_{i=1}^n \ln(3_{i-1})*3_i(x)[/tex]

Nasty looking thing. :yuck:

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- #19

i donot understand,ice breaker i do not buy your idea

- #20

LeonhardEuler

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- #21

What does this have to do with your "case" that a number is equal to any other?

- #22

- #23

What, I didn't have it before? All you have to do is apply the chain rule.

- #24

How many 3's are there?

- #25

and the last three carries the x.what i mean is the latter of leonhardeuler expression.

and i do not understand wat hypermorphism did

- #26

You can't have infinite 3's.

- #27

3^3^3^3^3^3^3^3...............

and the last 3 carries the x

and the last 3 carries the x

- #28

EL

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But if there's an infinite number of 3's, then there is no "last one".

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