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P.S. Can we say that a fraction like 1/3 is actually impossible ?
Originally posted by Benarius
[f(x + h) - f(x)]/h^2 as the limit of h--> 0
Wonderfull. I like your explanation of the limit.
Originally posted by Canopene
Apperently your not familar with (479001600 480000000) (362880/2=181440)(1000000-181440=-818560)(sqr75=8.6602540378443864676372317075294-8.18561=.474645ect)
reverse factor deteroation through polygonic breakdown of circles.
Originally posted by Sublime620
Just understand this:
They are always moving and growing.
1/infinity = 0
.999... = 1
Where did you get the idea that 1/infinity = 0?
The very sentence "1/infinity = 0" has no meaning. Why? Because
"infinity" is a concept, NOT a number. It is a concept that means
"limitlessness." As such, it cannot be used with any mathematical
operators. The symbols of +, -, x, and / are arithmetic operators, and
we can only use them for numbers.
To write 1/infinity and mean "1 divided by infinity" doesn't make any
sense. 1 cannot be divided by a concept. It can only be divided by
a number. Similarly, "infinity + 1" or "2 times infinity" are also
As another example, what does this mean: "1 / justice = 5"?
That's right! It is as meaningless as "1 / infinity = 0" because
justice is a concept, not a number.
In math, when you hear people say things like "1 over infinity is
zero" what they are usually referring to is something called a limit.
They are just using a kind of shorthand, however. They do NOT mean
that 1 can actually be divided by infinity. Instead, they mean that,
if you divide 1 by successively higher numbers, the result becomes
closer and closer to 0. If I divide 1 by a very large number, like a
billion, then I get one-billionth, which is a VERY small number, but
it isn't 0. Since there is no largest number, I can always divide 1 by
a bigger number. But that will just produce an even smaller number,
right? It will NEVER produce 0, no matter how high I go. But since the
answer to the division is getting closer to and closer to 0, we say
that "the limit of the expression is zero." But we have still not
divided anything by infinity, since that isn't a number.
To go back to your chocolate bar, what if you divide it among every
person living on earth? Each person would get roughly 1 six-billionth
of a chocolate bar. That's a very, very small amount, and you'd
probably need a microscope to see your piece, but it wouldn't be zero,
right? Ah, but you asked about dividing it up amongst an infinite
number of people. Well, we can't. Why? Because infinity isn't a
number, so you can't show me an infinite number of people. If you try
to, I will just add one more person, and then we'd realize that the
number you thought was "infinity" actually wasn't.
So, to finish up, you are perfectly correct in saying that "1/infinity
= infinitesimally small." But only if you realize that you REALLY mean
"1 divided by a REALLY big number is a REALLY small number."