Mike_bb's latest activity
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MMike_bb replied to the thread Undergrad ##x = z^y## can't be inverse function of ##y=\int_1^x \frac{1}{t}dt##.I wanted to prove that ##y=ln x## without using it as definition. It's not obvious for me that ##y=ln(x)##.
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MMike_bb replied to the thread Undergrad ##x = z^y## can't be inverse function of ##y=\int_1^x \frac{1}{t}dt##.I use definition: ##y=\int_1^x \frac{1}{t}dt##
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MMike_bb posted the thread Undergrad ##x = z^y## can't be inverse function of ##y=\int_1^x \frac{1}{t}dt## in Calculus.Hello! Some time ago I had a problem in understanding why ##x = z^y## can't be inverse function of ##y=\int_1^x \frac{1}{t}dt## I...
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MMike_bb reacted to Sagittarius A-Star's post in the thread Undergrad Why can coefficient "a" between spacetime intervals depend on velocity between systems? with
Agree.
No, see above in posting #35. -
MMike_bb reacted to Sagittarius A-Star's post in the thread Undergrad Why can coefficient "a" between spacetime intervals depend on velocity between systems? with
Like.
As written in the screenshot, this works because the transformation is linear. Therefore, you can re-write all primed variable in terms... -
MMike_bb replied to the thread Undergrad Why can coefficient "a" between spacetime intervals depend on velocity between systems?.Perhaps there is mistake in the book: Maybe: ##P=aT'^2+bX'^2+cY'^2+dZ'^2 +....##
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MMike_bb replied to the thread Undergrad Why can coefficient "a" between spacetime intervals depend on velocity between systems?.Hello! I read about irreducible polynomials and constant factor between them but it was written that polynomials were depended of the...
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MMike_bb replied to the thread Undergrad Why is ##x=e^y## the inverse of ##y=\int_1^x \frac{1}{t} dt##?.At the definition stage, we don't know that function ##y=e^x## satisfy to all pair of values ##(x,y)##.
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MMike_bb replied to the thread Undergrad Why is ##x=e^y## the inverse of ##y=\int_1^x \frac{1}{t} dt##?.Yes. But how do we know that there is not the pair of values ##(x,y)## for which ##y=e^x## isn't satisfied?
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MMike_bb replied to the thread Undergrad Why is ##x=e^y## the inverse of ##y=\int_1^x \frac{1}{t} dt##?.Yes. But that I have putted in my OP is already clear to me. Why can't I ask the second question here?
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MMike_bb replied to the thread Undergrad Why is ##x=e^y## the inverse of ##y=\int_1^x \frac{1}{t} dt##?.Not quite. I want to prove that the case ##x \neq e^y## for some ##(X_n;Y_n)## is impossible.
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MMike_bb reacted to PeroK's post in the thread Undergrad Why is ##x=e^y## the inverse of ##y=\int_1^x \frac{1}{t} dt##? with Agree.
That is precisely the question in your OP. I would forget ##\log## or ##\ln##. You have an integral function and the defining property...
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MMike_bb replied to the thread Undergrad Why is ##x=e^y## the inverse of ##y=\int_1^x \frac{1}{t} dt##?.bhobba, Ok. If we define ##log(x)=\int_1^x \frac{1}{t}dt## then it's necessary to prove that ##x=e^y## is really and that ##e## and...
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MMike_bb replied to the thread Undergrad Why is ##x=e^y## the inverse of ##y=\int_1^x \frac{1}{t} dt##?.How?? I want to define it as ##x=10^y## in such a manner. But it doesn't work. >>It is like force is defined as f=m*a, not suppose...
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MMike_bb replied to the thread Undergrad Why is ##x=e^y## the inverse of ##y=\int_1^x \frac{1}{t} dt##?.As I understand, we define ##ln(x)## as integral and then suppose that ##x=e^y## and further we find properties of ##e##.