Ternary! That was the word I was looking for... https://en.wikipedia.org/wiki/Three-valued_logic
Many thanks, @mchambin. In this household we believe the Number Theorists (such as Yours Truly) will solve the Problems of the Universe. The Physicists have little clue.
Who is the Mathematician's favourite Musician? J.S. Bach, of course.
https://www.bbc.co.uk/sounds/play/m001sf5j
The answer is 48.
Best, Steve.
Sorry Steve, you may not publish 0^0 = 1. Because, in correct mathematics it has no defined value.
One may write that the limit of x^x is 1 when x > 0 goes to 0. A correct proof is available on the net. A lot of BS too, handwaving if not plain wrong.
One may write x^0 = 1 for x > 0
One may write 0^x = 0 for x >0
( x positive not 0, whatever close to 0 )
No, I disagree, @mchambin.
n^o is quite continuous right along the real number line. It is one for positive values, but goes to complex values for negative n.
Any positive integer to the power zero is 1. A (gifted) child of ten knows this. You could probably apply L'hopital's rule also.
I have seen the graph. OK, it does a right angle turn at zero, but definitely goes through one at the point n = zero.
The matter is settled to my satisfaction. 😎
In latest Space News, an interesting debacle unfolding for the privately financed Peregrine moon lander.
It's sprung a fuel leak!
https://www.bbc.co.uk/news/science-environment-67915696
It's gonna crash and burn! Why am I not surprised? 😀
n^o is quite continuous right along the real number line. It is one for positive values, but goes to complex values for negative n.
Any positive integer to the power zero is 1. A (gifted) child of ten knows this. You could probably apply L'hopital's rule also.
I have seen the graph. OK, it does a right angle turn at zero, but definitely goes through one at the point n = zero.
The matter is settled to my satisfaction. 😎
In latest Space News, an interesting debacle unfolding for the privately financed Peregrine moon lander.
It's sprung a fuel leak!
https://www.bbc.co.uk/news/science-environment-67915696
It's gonna crash and burn! Why am I not surprised? 😀
x^x at 0.
No, it does not go througt 1 at x=0.
It all boils to at what goes on for x < 0 where one can only imagine analytic extensions.
x^y = e^y / Ln(x) has no extension at 0,0 . So there is no acceptable choice for any case. However some conventions are possible limited to well defined domains.
I looked at Wikipedia english version with Wikipedia french version.....There is contradiction on this issue.....Isn’t it funny ?
No, it does not go througt 1 at x=0.
It all boils to at what goes on for x < 0 where one can only imagine analytic extensions.
x^y = e^y / Ln(x) has no extension at 0,0 . So there is no acceptable choice for any case. However some conventions are possible limited to well defined domains.
I looked at Wikipedia english version with Wikipedia french version.....There is contradiction on this issue.....Isn’t it funny ?
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0^0 = 1 Is this true or false?
Why some people say it's true: A base to the power of 0 is 1.
Why some people say it's false: An exponent with the base of 0 is 0.
I read it in the Brilliant Math & Science Wiki - does it make any sense to you mathematicians?
I read further in the Brilliant Math & Science Wiki to find:
"The statement 0^0 = 1 is ambiguous and has been long debated in mathematics."
Apparently, this is mostly a matter of definition.
You'd better read the arguments for yourselves! https://brilliant.org/wiki/what-is-00/
"The statement 0^0 = 1 is ambiguous and has been long debated in mathematics."
Apparently, this is mostly a matter of definition.
You'd better read the arguments for yourselves! https://brilliant.org/wiki/what-is-00/
I looked at Wikipedia english version to compare with the Wikipedia french version.....There is contradiction on this issue.....Isn’t it funny ?
They are quitte différent and not only on this topic. Well, talk about a universal source of knowledge ?????
About x^x
The english version bluntly extend for x<0 the french version does not.
Galu said: Apparently, this is mostly a matter of definition. YES !
They are quitte différent and not only on this topic. Well, talk about a universal source of knowledge ?????
About x^x
The english version bluntly extend for x<0 the french version does not.
Galu said: Apparently, this is mostly a matter of definition. YES !
If the exponent n is positive (n>0), the nth power of 0 is 0.
If the exponent is negative (n<0), the nth power of 0 is undefined.
Or so I believe! 🤓
If the exponent is negative (n<0), the nth power of 0 is undefined.
Or so I believe! 🤓
Sounds like 0 again to me. LOL I can't understand why my calculator throws an error if I ask ln or log 0.
As @Mister Audio and @Galu discovered recently when making wrong statements about alleged "constant impedance adjustable L-Pads", it is extremely dangerous to argue with me about mathematical matters,
I don't mind revealing this, but the password to my stupid Android 12 mobile phone is 1729 (The Taxicab Number). What else could it be? I did consider -163 (another extremely interesting Heegner number) as a password, but couldn't find how to enter it. 🤣
I happen to know that 0! = 1 (Factorial n). I know that ln 0 (natural logarithm) is minus infinity.
I did get in a bit of a muddle about 0^n where n is negative. It must be infinity. 0^ -1 must be 1/0 for instance.
I realised where I got the notion of it going complex for negative exponents.
It is in the graph of the function x^x, which looks like this:
See it turns into a complex spiral for negative values, whilst being real for positive ones. Weird and unexpected.
One immediately spots a discontinuity in the differential coefficient, but not in 0*0 being equal to 1. QED (Quod erat demonstrandum) as we mathematicians are prone to say. 😎
I don't mind revealing this, but the password to my stupid Android 12 mobile phone is 1729 (The Taxicab Number). What else could it be? I did consider -163 (another extremely interesting Heegner number) as a password, but couldn't find how to enter it. 🤣
I happen to know that 0! = 1 (Factorial n). I know that ln 0 (natural logarithm) is minus infinity.
I did get in a bit of a muddle about 0^n where n is negative. It must be infinity. 0^ -1 must be 1/0 for instance.
I realised where I got the notion of it going complex for negative exponents.
It is in the graph of the function x^x, which looks like this:
See it turns into a complex spiral for negative values, whilst being real for positive ones. Weird and unexpected.
One immediately spots a discontinuity in the differential coefficient, but not in 0*0 being equal to 1. QED (Quod erat demonstrandum) as we mathematicians are prone to say. 😎
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I resent that as it was you who was making the wrong statements about L-pads!
You even admitted as much at the time!
Quote: "Mister Audio and @Galu. I am starting to think that you are right and I am wrong here on this L-Pad business." 😳
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I resent that as it was you who was making the wrong statements about L-pads!
You even admitted as much at the time!
Quote: "Mister Audio and @Galu. I am starting to think that you are right and I am wrong here on this L-Pad business." 😳
No. No. No. I was tempted to accord to weight of numbers as an opinion on adjustable L-Pads, but then realised I had been right all along.
There is no such thing as an adjustable Constant Impedance L-Pad. I decisively proved this with a thought experiment. A technique frequently employed by Mr. Einstein too.
I noticed you suddenly shutted up on the matter. Game, Set and Match to Portsmouth's own Autistic Sheldon Lee Cooper.
(I was watching Big Bang Theory this morning in an idle moment. The one where Penny is trying to get Bernadette off with Howard and Star Trek's "Sulu" aka George Takei is improbable romantic advisor on heterosexual matters.)
Best, Steve. (It's OK to be wrong sometimes....)
The fact of the matter is that it was I, not you, who made the final post on the topic in question.
We were having a discussion on whether the impedance an L-pad presents to the crossover, when controlling an 8 ohm speaker, remains constant.
I stated in that final post that the impedance was 8 ohm except at the middle setting where it was 11 ohm (based on the assumption that the L-pad resistance tracks were linear). In that we were in perfect agreement.
Remember, you only got your eye on the ball after you realised that that an L-pad was not a pot!
I found this about L pad:
https://www.electronics-tutorials.ws/attenuators/l-pad-attenuator.html
It considers an amplifier with an 8 ohm impédance.....Oh, well the author doesn’t know a real audio amplifier output has a near zeo impédance.
What a thick bla bla for just two resistors. There is much BS on the internet.
However it says:
The L-pad attenuator is an asymmetrical attenuator and therefore, if an attenuation network is required to match two unequal impedances in both directions, other types of attenuator such as the symmetrical “T-pad” or the “Pi-pad” attenuator should be used.
This is correct, removing the word "unequal".
https://www.electronics-tutorials.ws/attenuators/l-pad-attenuator.html
It considers an amplifier with an 8 ohm impédance.....Oh, well the author doesn’t know a real audio amplifier output has a near zeo impédance.
What a thick bla bla for just two resistors. There is much BS on the internet.
However it says:
The L-pad attenuator is an asymmetrical attenuator and therefore, if an attenuation network is required to match two unequal impedances in both directions, other types of attenuator such as the symmetrical “T-pad” or the “Pi-pad” attenuator should be used.
This is correct, removing the word "unequal".
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