one example would be 2x/x. If x = 0 one has 2x0/0 which equals 0/0. But what if you got very, very close to zero.. say, .002/.001 = 2. then .00002/.00001 = 2, .000000002/.000000001=2.. could you then say 0/0 = 2?
Since anything times 0 equals 0, 0/0 can equal anything (which is what they mean by "indeterminate."
Your example is a limit. It would be accurate to say that the limit of 2x/x, as x approaches zero, is 2, since no matter how close you get to zero (without actually getting there), the answer is 2. In old epsilon-delta terminology, for any epsilon difference from 2, I can give a delta difference from X=0 so that f(X+d) - 2 < e.
I didn't mention the limiting process in my intermediate algebra class. Every once in a while I like to give the students a peek into they might see in the next level..
we were simplifying rational expressions where one encounters 0/0 in many situations.
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Ham
one example would be 2x/x. If x = 0 one has 2x0/0 which equals 0/0. But what if you got very, very close to zero.. say, .002/.001 = 2. then .00002/.00001 = 2, .000000002/.000000001=2.. could you then say 0/0 = 2?
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GeorgeStGeorge
Since anything times 0 equals 0, 0/0 can equal anything (which is what they mean by "indeterminate."
Your example is a limit. It would be accurate to say that the limit of 2x/x, as x approaches zero, is 2, since no matter how close you get to zero (without actually getting there), the answer is 2. In old epsilon-delta terminology, for any epsilon difference from 2, I can give a delta difference from X=0 so that f(X+d) - 2 < e.
George
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waysider
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Ham
I didn't mention the limiting process in my intermediate algebra class. Every once in a while I like to give the students a peek into they might see in the next level..
we were simplifying rational expressions where one encounters 0/0 in many situations.
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GeorgeStGeorge
Most of those algebraic tricks, where you "prove" that 1 = 2, or such like, have steps involving dividing by zero (cleverly hidden, of course). :)
George
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Ham
Of course. :)
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