Exactly right!
Greg (Schindler)
Greg Hansen wrote:
Zero Ohms = Mathematically Incorrect
Aug 17, 2006
80 Replies
but 2a/a is always 2, so if a=0, then 0/0 = 2.
In other words, 0/0 is the limit of an infine number of equations, not all of which evaluate to 1.
John
They all evaluate to 1 if the numerator and the denominator are
identical. In your example:
2a
---- = 2
a
they are not, except when a = 0, in which case:
2a 2*0 0
---- = ----- = --- = 1
a 0 0
The proper procedure, in your example, should have been to multiply
the numerator _and_ the denominator by the same quantity,:
2a
---- = 1
2a
which would have eliminated the discontinuity going through zero.
Yoy bwon't find a mathematician to agree with you. And in most physical situations, the only sensible definition of 0/0 is "indeterminate."
Not all circulating current in superconductive rings is precisely 1 amp.
John
That doesn\'t mean I\'m not right.
Except the positive feedback rails the output. So the circuit makes no sense. It sure ain't a divider.
Not a divider either! More like a subtractor.
I agree that 0-0 = 0
Look closely at the text and the graphics. Both avoid a denominator of zero.
Jibberish.
John
You\'ve never heard of rail-to-rail outputs?
Run it in LTSPICE and then come back with your complaints, OK?
You\'ve never heard of rail-to-rail outputs?
Run it in LTSPICE and then come back with your complaints, OK?
0/0=1 is sorta like the question of where is the extra dollar? 3 guests check into a $30 hotel room and each pays $10. The hotel clerk later realizes he overcharged the guests since the room was only $25 instead of $30. So, the clerk sends the bellhop to the room to refund the extra $5 and each guest takes $1 and the bellhop gets a $2 tip. Therefore, each guest has payed $9 for a total of $27 and the bellhop got a $2 tip, bringing the total expenses to $29.
But the room was $30 paid in advance, so what happened to the extra dollar?
-Bill
That had me thinking for a while, but the way I figure it, each guest has ended up paying £9, totalling £27 :- £25 for the room, and £2 for the bellhop.
The £2 belhop tip was deducted from the £27 total expenses, and not added on afterwards.
depends which way round you think of it.
I missed that earlier. (that part of your post, Not Analog Devices\'
stuff)
The reason they avoid it is because of hardware problems, not that
there\'s anything wrong with the concept.
Yes. From an engineering prespective, 0/0 means "there's not enough signal to tell what's actually going on, so find some other way to measure things here."
John
I don't need Spice to tell me that both opamps are always railed! Or what the voltage at QUOT will be if the obvious fixes were made; and that won't be +1.
It's self-explanatory.
John
If you think they are, then you do.
Don't need to in this instance.
Flail away. But the opamp circuit is still railed.
John
for
Yes, something like that. Another one I heard years ago was finding a counterfeit coin amongst 12 coins using a balance scale 3 times.
One of 12 coins is counterfeit and weighs more or less than a good coin. How do you find the counterfeit coin using a balance scale 3 times?
For example, if you weigh 6 coins against the other 6, the scale will not balance, and tells you nothing.
How can you find the counterfeit coin with only 3 weighings?
I forget the answer.
-Bill
One of 12 coins is counterfeit and weighs more or less than a good coin. How do you find the counterfeit coin using a balance scale 3 times?
For example, if you weigh 6 coins against the other 6, the scale will not balance, and tells you nothing.
How can you find the counterfeit coin with only 3 weighings?
I forget the answer. ===============================================
formatting link
Run the simulation.
---
+V +V | | | +---|--[R]--+ +---|-[10R]-+ | | | | | | 1V--[R]--+--|+\\ | NOM>----[R]--+--|-\\ | | >-----+-->QUOT | >-----+--------------|-/ DENOM>--[R]--+--|+/ | | | | [10R] | | | | | 0V -V -VHappy now?
-- John Fields Professional Circuit Designer
+V +V | | | +---|--[R]--+ +---|-[10R]-+ | | | | | | -1V--[R]--+--|+\\ | NOM>----[R]--+--|-\\ | | >-----+-->QUOT | >-----+--------------|-/ DENOM>--[R]--+--|+/ | | | | [10R] | | | | | 0V -V -V
Happy now?
John Fields
Professional Circuit Designer
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