Math makes me happy

[Flying Mullet]

See? You're using the logic that .000...1 is illogical, Or incorrect, or whatever term you want to use. Personally, I don't see it any different.

Actually I posted those definitions because you said that .000..1 is infinite, and I was showing you why it isn't. I never said anything about anything being logical or illogical.

I was thinking that the lim (1/x + 1) x-> ∞ was greater than one, but wrote it as less. MY MISTAKE

How could you! :surprised

[Peegee]

You know what? I have no idea!

[eestlinc]

i'm not going to read this entire thread, but .999... = 1

proof

8/9 + 1/9 = 1

. .88888888888888888...
+ .11111111111111111...
.99999999999999999...

[SeeDRankLou]

SeedRankLou: Simplifying the final solution makes sense (and makes things more readable too), although I wouldn't say working in simplest terms all the time is necessary during the working out stage of your solution.

and one of them is that all terms and equations must end as their simplest form.

That applies in no way to intermediate steps. I agree with you completely. In fact, there exist many equations that can only be solved by not simplifying terms in intermediate steps.

To Flying Mullet, Moo Moo the New Cow, and omnitarian: The idea of the numbers .999.... and .000....1 being infinite are very fiesible, if written correctly.

(Please forgive these equations, I don't know how to type math symbols)
.999....=(Reiman Sum) 9/(10^n) where n goes from 1 to infinity.
.000....1=1/(10^infinity)

[Endless]

0.999... = 9*0.111... = 9*1/9 = 1
or
0.999... = 0.333...+0.333...+0.333... = 1/3+1/3+1/3 = 1
or
1-0.999... = 0.000..., but a number with an infinity of 0 is 0, so 1-0.999...=0 and 1=0.999...
or x=0.999...
10x=9.999...
10x-x=9
9x=9
x=1

There are many ways to prove it, but I can't be arsed to compile them all.

[Flying Mullet]

.000....1=1/(10^infinity)

Is the result of dividing a number by an infinite number an infinite number?

I don't know the answer. Maybe someone else does.

[SeeDRankLou]

I would image it would be an infinitely small number, give that the denominator is infinity. The closest number to zero without being zero.

Edit: But on that note, I guess the 1 could be replaced with any number greater than zero that isn't infinity, and 10^infinity could just be replaced with infinity.

[Peegee]

It really doesn't matter since ∞ isn't a number per se, so arithmetic operations involving it typically result in ∞ anyway :D (meaning 1 + ∞ = ∞, ∞ / ∞ = ∞ .. etc)

wait ∞ / ∞ = ∞ ? x / x = 1 only for { x | x є R } ?

:o

[SeeDRankLou]

Infinity is the idea of a number that nothing is greater than, which does not exist. Still, the concept of infinity can be computed in arithmetic operations. And furthermore, the idea of infinity still fits into the realm of real numbers. Depending on certain factors, infinity/infinity=1 is correctly. Just like 1/infinity would be the smallest fiesible number possible, since you would be having the largest possible denominator.

[Dr Unne]

A rational number is a number capable of being expressed as an integer or a ratio of two integers, excluding zero as the denominator. That distinction is made for a reason. --SeedRankLou

No reason that I know of. All numbers capable of being expressed as an integer (x) are also capable of being expressed as a ratio of two integers, namely x/1. The part you added to the definition is redundant.

Just like 1/infinity would be the smallest fiesible number possible, since you would be having the largest possible denominator.

Which number system are you using? Infinity is not a real number, and it can't be used as a number. 1/oo is undefined. Limit (x->oo) 1/x is the closest idea to that, that I know of. You might as well ask what 1/BLARJG means.

[Peegee]

what does 1/BLARJG mean, Dr Unne? :eep: :love: :mad: :greenie: :rolleyes2 :( :p :D

[Del Murder]

The great thing about math is that it is not subjective.

∞ is not a number, it is a concept. Therefore, 10^∞ is not a number and cannot be used as such.

Lou: You said 'simplest terms' is part of a sort of 'math etiquette' and I could not agree with you more. The important thing to remember here is that etiquette is used for cleanliness and not for substance.

[Yamaneko]

I always thought whenever we were told to put things in "simplest terms" it was to make us work more and make the teacher's job easier. Of course, I've never used math in real world problems that deemed the use of converting an answer to simplest terms, so I'm guessing that using simplest terms makes everyone's job easier.

Small numbers are better than big ones, I think.

[Peegee]

btw what *is* the practical use of calculus?

[eestlinc]

one practical use of calculus is determining rates of change, like acceleration. also area under a curve, which is useful in statistical analysis.