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The Sedin's 6th Sense

Simplest Yet One of the Toughest Math Questions I've Seen

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That's not how logic works. This isn't a "conspiracy theory" nor is it "magical". It is stone cold, objective reasoning.

How about this? All fractions with 7 as a denominator have an interesting property: they use the same 6 repeating numbers in the same order but with a different starting place).

1/7 = 0.142857 142857.... (the 142857 repeats)

2/7 = 0.285714 285714.... (the 285714 repeats)

and so on. It turns out that 6/7 = 0.857142 857142.... (the 857142 repeats).

Now watch this:

1/7 = 0.142857 142857...

+ 6/7 = 0.857142 857142...

-----------------------------------

1 = 0.999999 999999...

If that doesn't convince you then what will?

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And you're wrong about this also. The decimal 0.3333.... continued to an infinite number of decimal places is EXACTLY 1/3. It's only when we round to a finite number of decimal places (usually for purposes of doing a calculation) does it become an approximation.

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No, 0.33333 repeating is the closest approximation you can have of 1/3 in a base 10 number system. any repeating value is an approximation. Try the same tricks in base 12 notation and it doesn't happen.

In base 12, it goes

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A B, 10, 11, 12 etc

in base 3, 1/3 = 0.4. Exactly 0.4.

A similar conversion of 0.9999_ to binary will poke holes in that little trick.

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The problem with the 7 and 3 decimal series, is that you can only get close to the actual value, never getting exactly there.

For example, some say 1/3 equals .33, well that is close but not accurate. .333 is closer, but still not there. .333333333 is closer still, yet it is still not completely accurate because the 3's go on for infinity. For every 3 added, you get closer to the actual value but will never get there.

So, when you take this back to the .999 you can see that every 9 added gets the value closer to the actual value, but won't get the actual value

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So what? We're talking about the infinite series 0.3... in base 10.

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The problem with the 7 and 3 decimal series, is that you can only get close to the actual value, never getting exactly there.

For example, some say 1/3 equals .33, well that is close but not accurate. .333 is closer, but still not there. .333333333 is closer still, yet it is still not completely accurate because the 3's go on for infinity. For every 3 added, you get closer to the actual value but will never get there.

So, when you take this back to the .999 you can see that every 9 added gets the value closer to the actual value, but won't get the actual value

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If you never get to the actual value of 1, then why is it that when you subtract 1 by .9999999 repeating you will get 0. It is because the two numbers are the same, as infinity makes up the difference.

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That's not how logic works. This isn't a "conspiracy theory" nor is it "magical". It is stone cold, objective reasoning.

How about this? All fractions with 7 as a denominator have an interesting property: they use the same 6 repeating numbers in the same order but with a different starting place).

1/7 = 0.142857 142857.... (the 142857 repeats)

2/7 = 0.285714 285714.... (the 285714 repeats)

and so on. It turns out that 6/7 = 0.857142 857142.... (the 857142 repeats).

Now watch this:

1/7 = 0.142857 142857...

+ 6/7 = 0.857142 857142...

-----------------------------------

1 = 0.999999 999999...

If that doesn't convince you then what will?

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Checkmate. Another good explanation.

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Both actually

Edit: I don't know myself who's right and who's wrong, but babych and others have gave great explanations to support their opinions. You asked for a number other than a multiple of 3 and if proven, you'd give in yet after doing that, its still not enough...I don't know who's right or wrong like I said before, but if you wanna make your point, dot argue it, show it like how babych has which his explanations have convinced me.

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You completely missed the point, unless you have a calculator that goes to the infinte decimal point to prove me wrong. .999999999 is an estimate, close to the actual value but not there

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What you fail to realize is in order for two real numbers to be different in value, there has to be an infinte amount of real numbers in between. Try to name a real number that greater that .99999 repeating and less than 1. It is simply not possible, as they are the same.

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Who has a background in calculus? Isn't this a limits issue?

As you increase the digits behind .9999999999...... to infinity, the number gets infinitely closer to 1.

So .9999999999.... = 1, sicne as you add 9 to infinity, the difference between .9999999.... and 1 gets infinitely smaller and approaches zero. Mathematically, they are the same thing.

At least this is what I remember from calculus.

Wikipedia says I'm right too: http://en.wikipedia.org/wiki/0.999

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Who has a background in calculus? Isn't this a limits issue?

As you increase the digits behind .9999999999...... to infinity, the number gets infinitely closer to 1.

So .9999999999.... = 1, sicne as you add 9 to infinity, the difference between .9999999.... and 1 gets infinitely smaller and approaches zero. Mathematically, they are the same thing.

At least this is what I remember from calculus.

Wikipedia says I'm right too: http://en.wikipedia.org/wiki/0.999

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You are absolutely correct, I tried explaining it numerous times:

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Who has a background in calculus? Isn't this a limits issue?

As you increase the digits behind .9999999999...... to infinity, the number gets infinitely closer to 1.

So .9999999999.... = 1, sicne as you add 9 to infinity, the difference between .9999999.... and 1 gets infinitely smaller and approaches zero. Mathematically, they are the same thing.

At least this is what I remember from calculus.

Wikipedia says I'm right too: http://en.wikipedia.org/wiki/0.999

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This just goes back to the limitations of decimals that I've been talking about this entire time. If you fail to accept decimals as an imperfect way of describing fractions, then you will always reach your conclusion of them being equivalent. However, if you see the problem with a decimal representing something that goes on for infinity, then my conclusion is the logical one.

This is my conclusion from this debate that has gone on for too long. 2 conclusions can be reached, it just depends on how one views decimals that decides which one is chosen.

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