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Why x*0 = x
#31
RE: Why x*0 = x
If you disagree with 0.99999...=1, you have no business talking about algebra and calculus Wink
The fool hath said in his heart, There is a God. They are corrupt, they have done abominable works, there is none that doeth good.
Psalm 14, KJV revised edition

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#32
RE: Why x*0 = x
OH SNAP
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#33
RE: Why x*0 = x
(December 13, 2015 at 2:59 pm)Quantum Wrote: If you disagree with 0.99999...=1, you have no business talking about algebra and calculus Wink

Then they can be substituted for each other in all cases which is false, but that would be an argument for a different thread, though it would not progress any further than "there is a god / there is no god".  Been there, done that.
You make people miserable and there's nothing they can do about it, just like god.
-- Homer Simpson

God has no place within these walls, just as facts have no place within organized religion.
-- Superintendent Chalmers

Science is like a blabbermouth who ruins a movie by telling you how it ends. There are some things we don't want to know. Important things.
-- Ned Flanders

Once something's been approved by the government, it's no longer immoral.
-- The Rev Lovejoy
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#34
RE: Why x*0 = x
(December 13, 2015 at 4:20 pm)IATIA Wrote:
(December 13, 2015 at 2:59 pm)Quantum Wrote: If you disagree with 0.99999...=1, you have no business talking about algebra and calculus Wink

Then they can be substituted for each other in all cases which is false, but that would be an argument for a different thread, though it would not progress any further than "there is a god / there is no god".  Been there, done that.

Sorry, now you have my attention. Give me one example where they make a difference, and Ill go back on topic!
The fool hath said in his heart, There is a God. They are corrupt, they have done abominable works, there is none that doeth good.
Psalm 14, KJV revised edition

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#35
RE: Why x*0 = x
(December 13, 2015 at 4:20 pm)IATIA Wrote:
(December 13, 2015 at 2:59 pm)Quantum Wrote: If you disagree with 0.99999...=1, you have no business talking about algebra and calculus Wink

Then they can be substituted for each other in all cases which is false, but that would be an argument for a different thread, though it would not progress any further than "there is a god / there is no god".  Been there, done that.

I'm with Quantum. Give us an example of where substituting them doesn't work.

0.999... Is equal to 1. Most people who don't accept this probably don't know know what mathematicians mean when they say that. It doesn't mean the numbers are the same, because of course they are different numbers, but the value which the number represents is the same.

Just like 2/2 is equal to 1. Different numbers, same value.

If you think 0.999... and 1 are different values, then there must be a value which lies between them. What is it? Try as hard as you can, you won't be able to find another value which fits between 0.999... and 1, therefore they are the same value.

Another way to think about it is this:

1/3 = 0.333...
Multiple each side by 3.
3 x 1/3 = 3 x 0.333...
1 = 0.999...
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#36
RE: Why x*0 = x
(December 13, 2015 at 1:18 pm)IATIA Wrote: If you take 0 books out of the pile, you will eventually have an infinite number of piles of no books.

If 0.999... =1 (which I adamantly disagree with)
Then 10/infinity=0 (by the same 'rule' that allows 0.999... to equal 1)
Therefore 10/0=infinity.

But if you multiply both sides by 0, then 10 = 0. (another reason that 0.999... doe not equal 1)

If you take 0 books out of the pile, you will eventually have 1 pile of 10 books, and an infinite pile of 0 books (or you can say you start with that too). Either way, there's still a pile of 10 books.

You can't just ignore that!
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#37
RE: Why x*0 = x
[Image: 0.999_1.png]


0.999... is valid

1 results in an indeterminate number.

The problem is basically apples and oranges.
You make people miserable and there's nothing they can do about it, just like god.
-- Homer Simpson

God has no place within these walls, just as facts have no place within organized religion.
-- Superintendent Chalmers

Science is like a blabbermouth who ruins a movie by telling you how it ends. There are some things we don't want to know. Important things.
-- Ned Flanders

Once something's been approved by the government, it's no longer immoral.
-- The Rev Lovejoy
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#38
RE: Why x*0 = x
(December 13, 2015 at 5:07 pm)IATIA Wrote: [Image: 0.999_1.png]


0.999... is valid

1 results in an undefined number.

The problem is basically apples and oranges.

No. It only gives you a valid answer if you don't just plug in .9999... but secretly pull the limit of the geometric series upfront.
If you plug in 0.999999... it is invalid because .99999...-1=0 in the denominator. (see Tibs statement below)

What you apparently would like to do, which is a different thing mathematically, is plugging in .9999999...9999 with a finite number of n digits, and only then take the limit n->infty of the whole fraction afterwards. THEN you get a finite limit for your fraction. But this is just one of many ways to calculate the limit lim_x->1 f(x) and does not mean that .999.... somehow is a different real number than 1.

I am not aware that f(.9999.....) has ever been used as a shorthand for lim_x->1 f(x), which is what you would like to define it as, as far as I can tell. It is instead f(lim_x->1 x) which is equivalent to f(1). If you want to define periodic decimals as indicating delayed limits, you are using a different terminology than any mathematics text I know. To express such things, 0+ and 0- are usually used.
The fool hath said in his heart, There is a God. They are corrupt, they have done abominable works, there is none that doeth good.
Psalm 14, KJV revised edition

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#39
RE: Why x*0 = x
(December 13, 2015 at 4:56 pm)Tiberius Wrote: If you take 0 books out of the pile, you will eventually have 1 pile of 10 books, and an infinite pile of 0 books (or you can say you start with that too). Either way, there's still a pile of 10 books.

You can't just ignore that!

Which is why x/0 is undefined and invalid.

[Image: 0.999%202.png]
You make people miserable and there's nothing they can do about it, just like god.
-- Homer Simpson

God has no place within these walls, just as facts have no place within organized religion.
-- Superintendent Chalmers

Science is like a blabbermouth who ruins a movie by telling you how it ends. There are some things we don't want to know. Important things.
-- Ned Flanders

Once something's been approved by the government, it's no longer immoral.
-- The Rev Lovejoy
Reply
#40
RE: Why x*0 = x
(December 13, 2015 at 5:07 pm)IATIA Wrote: [Image: 0.999_1.png]


0.999... is valid

1 results in an indeterminate number.

The problem is basically apples and oranges.

0.999... isn't valid in that formula.

Look at the denominator, 0.999... - 1. The result of that is going to be the difference between 0.999... and 1, correct? Well, what is the difference between 0.999... and 1? What must you add to 0.999... to get 1?

0.000...1? That's an invalid number. You can't have an infinite string of zeroes, and then a 1, at least not in regular math, because then the infinite string of zeroes isn't infinite, it's finite.

So the difference between 0.999... and 1 is 0, so the denominator is equal to 0, which means the formula results in an invalid number.

The problem isn't apples and oranges, it's apples and apples, because the two numbers have the exact same value. Unless you can show us that the denominator equals something else, you have no argument.
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