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Assume v. Presume

MikeSh said:
OK. But the point stands that 0 can be repeated an unlimited number of times without reaching 1, or any other value.
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The correct interpretation is that x×0=1 has no solutions for x. Infinity never enters the mathematics.
 
EEPhil said:
Not in all branches of mathematics. eg. Riemann sphere: 1/0 = infinity, 0/0 undefined. :D
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True, we mathematicians are such sophists, but what I said goes in normal usage. Fitting this definition to BH's example would be difficult.:whistling::whistling:
 
Mike0001 said:
True, we mathematicians are such sophists, but what I said goes in normal usage. Fitting this definition to BH's example would be difficult.:whistling::whistling:
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Try being an electrical engineer. We replace i by j, so as not to confuse imaginary terms with current. No I don't mean jnfjnjty.:rolleyes:
We also have conductivity and resistivity, one being the inverse of the other. Even worse, something with zero resistance (which probably doesn't exist unless you believe in metallic hydrogen) is said to have infinite conductivity! The point being, engineers believe 1/0 = infinite even if mathematicians don't.:confused:
 
gomezz said:
You can make 0/0 come out as anything you like depending on how you sneak up on it! :D
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But strictly speaking, you should not use the expression. Division by 0 is forbidden.

See the definition of a field. F\{0} is an abelian group under multiplication.
 
EEPhil said:
engineers believe 1/0 = infinite even if mathematicians don't.:confused:
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Engineers are practical people, able to be pragmatic. Mathematicians would never get anything done if left to their own devices, agonising over whether every last aspect was properly defined and valid. Pragmatically, 1/∞︎ ≋︎ 0 whichever way you cut it, therefore 1/0 ≋︎ ∞︎ and we don't really care what kind of infinity it is.
 
"The train line is closed between Swindon and Gloucester following the collision between a train and a car near Frampton Mansell yesterday" (I paraphrase). :mad:
 
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Black Hole said:
Sure he wasn't more interested in the process than the result?
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Probably. But his background was mathematics.
Having said that, I've come across many engineers who get so worked-up about the maths they never get anything done (or can't explain what they've done so that ordinary mortals can understand it).
 
EEPhil said:
Is this what you mean:
http://web.physics.ucsb.edu/~lecturedemonstrations/Composer/Pages/64.42.html ?
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Not if I understood the intention of Trev's post correctly.

For a thin resistive film (like one might make resistors from, typically as a spiral pattern around a cylindrical former), the longer the conductive track is the greater its end-to-end resistance. However, the wider the track is, the lower its end-to-end resistance (equivalent to putting more resistors in parallel). The two balance out, and the unit of surface resistance is ohms per square (it doesn't matter how big the square is, it will have that same resistance measured from one side to the opposite side, assuming the zero-resistance contact extends the length of each side).

This is easy to visualise: take a square of resistive film; make it a rectangle by doubling the length and the resistance must double, make it a square again by doubling the width and the conductivity doubles (ie the resistance halves) so the overall resistance is the same as it was before.

Now let's think about the third dimension: a cube. Suppose the surface-to-surface resistance through its volume is R. Double the resistive length and the resistance doubles to 2R. However, double the resistive area and the conductivity increases by a factor of 4 (the resistance is quartered), so the overall resistance is ½R. So no, "ohms per cube" does not work (ie is not constant for any particular resistive material).
 
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Black Hole said:
Engineers are practical people, able to be pragmatic. Mathematicians would never get anything done if left to their own devices, agonising over whether every last aspect was properly defined and valid. Pragmatically, 1/∞︎ ≋︎ 0 whichever way you cut it, therefore 1/0 ≋︎ ∞︎ and we don't really care what kind of infinity it is.
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There are loads of bogus and incorrect arguments based on such slapdash reasoning. If you discard rigour, as with word meanings, you can never be sure what you end up with. :duel:
 
EEPhil. Yes, that's the one.
Black Hole said:
Not if I understood the intention of Trev's post correctly.
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How do you know what I intended?:o_O:
Black Hole said:
However, double the resistive area and the conductivity increases by a factor of 4, so the overall resistance halves. So no, "ohms per cube" does not work.
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OK, you win. It was obviously my faulty memory of the resistor cube puzzle highlighted by EEPhil that I was 'remembering' from my early learning days many years ago. :oops:
 
Black Hole said:
"The train line is closed between Swindon and Gloucester following the collision between a train and a car near Frampton Mansell yesterday" (I paraphrase). :mad:
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You mean you can't buy cheap train tickets (from The Train Line) between those stations?
 
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