What if X=1 and Y=1, doesn’t X*Y=X/Y
Or, for that matter, X=anything and Y=1.
I just did a quick look through the posts, and here’s my theory… I’m not a mathematician, so don’t get annoyed or anything.
The reciprocal of infinity has to be 0 because one over an infinitely large number would be so small that it would equal 0, just as the repeating decimal .999 would be equal to 1.
If the reciprocal of infinity is 0, wouldn’t it follow that the reciprocal of 0 is infinity?
“[He] beat his fist down upon the table and hurt his hand and became so
further enraged… that he beat his fist down upon the table even harder and
hurt his hand some more.” – Joseph Heller’s Catch-22
The reciprocal of infinity is actually a limit, and not a discrete computation. The reciprocal of zero is , he he, undefined. Sorry, you can’t get around this. Ahhh, what pleasure it must be to be undefined? But, anyway, there are limits where the denominator approaches zero, these expressions go to infinity.
By the way, I’d like to say that Lynne has just a great way of explaining this stuff. I wish I had a teacher like that.
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Oh yeah, as for the x*y can never equal x/y:
Setting x*y = x/y gives us
y^2 = 1.
y = 1 or -1 and x can be any real number.
I’ll get out of the upholstery now. 
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Sorry, one more thing. As for Calculus being useless, I agree. But then, so is the Mona Lisa.
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<< The reciprocal of infinity has to be 0 because one over an infinitely
large number would be so small that it would equal 0, just as the
repeating decimal .999 would be equal to 1. >>
I dunno how many times some people need to be told something before it penetrates that thick skull. If you look at a sequence of numbers, 1/N, where N gets larger and larger and larger, you can see that the fraction 1/N gets smaller and smaller and smaller, ever closer to 0… approaching zero as a limit, but NEVER equaling zero, for the reasons lynne gave.
And zero is not simply “no-thing.” Zero is the additive identity under the group operation of addition in the number system. Sheeesh.
WiseOldMan said:
What if X=1 and Y=1, doesn’t X*Y=X/Y
*What about this:
If x=2 and y=2 then
x + y = x * y = x[sup]y[/sup]
Deep, eh?*
This might be a bit late, but:
L’hospital rule is not applicable when either the N or D or N’ or D’ (the derivative) is undefined, ie, 0 or infinity.
Math is a rigid subject. It NEVER fails. If it does (as in division by zero), disallow the opertaion and you are fine.
Veera, would you care to explain L’Hopital’s rule to the audience please? I think I may just have to s#!tcan my Calculus textbook, along with all the other ones around the office.
I hope I will get it right THIS time:
Assume you have N(x)/D(x), where N and D are dependent on x.
If you want N(a)/D(a), where a is a constant, we just calculate N(a) and D(a). BUT if N(a) and D(a) is singular, the ratio has no meaning.
If all you want is just the limit of the ratio as x tends to a, the L’Hospital rule says the limit is N’(a)/D’(a). If N’(a) or D’(a) is again singular, oops!!
Was that enuf? Basically, division by zero is undefined because its nonsense.
Now, someone please reply to my mints and impotency query. That has been playing on my mind more that /0!!!
Strainger, you don’t need to shitcan the calc book; you had it right. I think what veera1’s getting at is that L’hopital’s rule doesn’t apply when either the numerator or the denominator but not both tend toward zero or infinity. For example, we can’t (and don’t) apply it in the case of say 3/x as x goes to zero, so it can’t be used to answer the question “what’s 3 over 0”? It does apply to something like 3x/x as x approaches zero, which is one of the forms (0/0) you stated. Also, if you should happen to get N’/D’, and still have both heading towards 0/0 or inf/inf, you can apply L’Hopital’s rule again.
(Not sure what provoked the resurrectuion of this topic, but what the hell…)
I was just being sarcastic about shitcanning the Calculus book, Lynne. Veera just sounded like he was way out in left field and I chose to be a smart-ass about it. I do remember L’Hopital’s rule pretty well. Occasionally, you run into an instance of N(x)/D(x) -> 0/0 or infinity/infinty no matter how many derivatives you take, in which case, IIRC, you call it “undefined” and move on to the next homework problem.
By the way Veera, given the number of mints you eat per day, I’d say that you are probably the best experiment regarding the mints/impotency question. If your Mr. Happy still works right, I’d say your friend was B.S.ing you and that mints do not cause impotency. Seeing Dennis Franz’s butt on NYPD blue on the other hand …
(my apologies for answering this in the wrong thread)
…but MUCH more entertaining…perhaps we should rephrase this as “does attempting to divide by zero cause impotency?” I claim only if you do it excessively.
Lynne, so now I know what those Calculus teachers were trying to do to me! Academic saltpeter! Farging bastages.
When you divie a number by 1, you get the number. If you divide the number by .1, you get a higher number (10 times higher), if you divide it by .01, the result is even higher, and so on. The closer you get to 0, the closer you get to infinite…so why doesn’t x/0=infinite?
Well, here’s what I think…try the same thing, only divide by negative numbers. The closer you get to 0, the lower the number gets, and the closer it gets to “negative infinite” (Okay, so there is no such thing as negative infinite, but there isn’t such a thing as positive infinite either.)
Since 0 is neither positive nor negative, then we can say that x/0 = x/-0. If x/0 = infinite, then x/0 would also equal negative infinite, which would make it impossible to do.
There is one exception, though. It is possible to divide by zero in one condition. 0/0. Zero divided by itself has the solution of all real numbers, because for any number, if you multiply it by zero again, the answer is zero!
I have another point that is kinda irrelevant, but still wierd to think about. What is infinite divided by infinite? The first answer that comes to your mind is 1, but is that the answer? If you take any positive number and multiply it by infinite, the answer is infinite, so would the answer to infinite / infinite be any real number greater than 0? Geh. I’ve got a headache now.
0/0 and infinity/infinity are also forbidden, and for the same reason. If they are allowed, then you can prove that 1=2.
0*infinity and several other cases are forbidden, as well.
John W. Kennedy
“Compact is becoming contract; man only earns and pays.”
– Charles Williams
Oh, for the love of God, people. Please refer to the posts by AuraSeer posted 06-10-99 02:30 PM, me posted 06-10-99 04:30 PM , and lynne posted 06-10-99 05:19 PM. If you’re really interested in more details about Messr. L’Hopital’s wonderful rule, I can detail it even further.