0.99~=1 - Page 2 - Electronic Circuits Projects Diagrams Free

gramo · 18th April 2007, 02:31 PM

... And the result is lol?

(1+1/∞)^∞

(1+0)^∞

(1)^∞

1?

Optikon · 18th April 2007, 08:08 PM

1 + X = X for large values of X
1 + 2 = 2 for large values of 2

gramo · 19th April 2007, 12:21 AM

Quote:

Originally Posted by Optikon

1 + X = X for large values of X
1 + 2 = 2 for large values of 2

Why does 1 + X = X?

What’s the analogy behind it?

Sceadwian · 19th April 2007, 12:32 AM

If X is infinity.

gramo · 19th April 2007, 12:40 AM

That’s understandable, because Infinity is an undefined value.

But 'large' values of 2 does not.

1 + 2 = 4 For large values of 2

Because 2.99' can be thought of as 3, as its always drawing closer to 3,

so 1 + 3 = 4

arod · 19th April 2007, 12:55 AM

Quote:

Originally Posted by ljcox

0.9999 approaches 1 as the number of decimal places approaches infinity.

0.3333 approaches 1/3 as the number of decimal places approaches infinity.

End of story.

0.33... = 1/3. You are trying to quantify infinity in your definition.

dknguyen · 19th April 2007, 04:20 AM

0.999...~= 1? Yes!
0.999... = 1? No.

End of story. If you do write down 1 in your calculations, it's because the difference is so small it doesn't matter (same reason why we round numbers).

Pommie · 19th April 2007, 07:58 AM

Quote:

Originally Posted by gramo

... And the result is lol?

(1+1/∞)^∞

(1+0)^∞

(1)^∞

1?

The result is e (2.71828). Try setting infinity to 1 then 10, 100, 1000, 10,000 etc. The graph levels out at e.

Mike.

ljcox · 19th April 2007, 09:08 AM

Quote:

Originally Posted by arod

0.33... = 1/3. You are trying to quantify infinity in your definition.

I did not say that 0.33... = 1/3. I said it approaches 1/3 as the number of decimal places approaches infinity.

No, I'm not trying to quantify infinity, I'm simply stating a mathmetical fact.

You can't quantify infinity, you can only approach it.

ljcox · 19th April 2007, 09:11 AM

Quote:

Originally Posted by dknguyen

0.999...~= 1? Yes!
0.999 = 1? No.

End of story. If you do write down 1 in your calculations, it's because the difference is so small it doesn't matter (same reason why we round numbers).

If you read the original question it was "0.99 -continuious- = 1" and the answer is no. Rounding up is a different issue.

ljcox · 19th April 2007, 09:20 AM

Quote:

Originally Posted by gramo

... And the result is lol?

(1+1/∞)^∞

(1+0)^∞

(1)^∞

1?

You can't divide by infinity or raise a number to the power of infinity.

If x = 1/n then x approaches 0 as n approaches infinity.

If x = 1^n then x =1 for all n. But n = ∞ is not valid. n can only approach ∞.

Pommie · 19th April 2007, 11:14 AM

And, as X approaches infinity then (1+1/X)^X approaches e.

Mike.

arod · 19th April 2007, 11:38 AM

Quote:

Originally Posted by ljcox

I did not say that 0.33... = 1/3. I said it approaches 1/3 as the number of decimal places approaches infinity.

No, I'm not trying to quantify infinity, I'm simply stating a mathmetical fact.

You can't quantify infinity, you can only approach it.

0.33~ = 1/3 => That is mathematical fact. What could it possibly be "approaching?" Here is one of many proofs:

c = 0.999~
10c = 9.999~
10c - c = 9.9999~ - 0.999~
9c = 9
c = 1

Hard to argue with that. Whether you want to believe it or not, this is accepted by all mathematicians. If you still don't want to believe me, I will show you the convergence of the infinite geometric series when I get home later today.

gramo · 19th April 2007, 12:00 PM

Quote:

Originally Posted by Pommie

And, as X approaches infinity then (1+1/X)^X approaches e.

Mike.

umm, where did e come from?

Pommie · 19th April 2007, 02:34 PM

The natural constant e is the amount in billions of dollars that google was valued at when it floated on the NYSE. It is also the base of natural logarithms. See wiki.

In fact they define e as,

Mike.

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18th April 2007, 02:31 PM	(permalink)
gramo	... And the result is lol? (1+1/∞)^∞ (1+0)^∞ (1)^∞ 1? __________________ Spency. PIC Micro's - Your mind is the limit PIC's and interfacing with other devices - a PIC Basic Guide @ digital-diy.net Last edited by gramo; 18th April 2007 at 02:35 PM.

18th April 2007, 08:08 PM	(permalink)
Optikon	1 + X = X for large values of X 1 + 2 = 2 for large values of 2

19th April 2007, 12:32 AM	(permalink)
Sceadwian	If X is infinity. __________________ "Because I be what I be. I would tell you what you want to know if I could, mum, but I be a cat, and no cat anywhere ever gave anyone a straight answer, har har."

19th April 2007, 12:40 AM	(permalink)
gramo	That’s understandable, because Infinity is an undefined value. But 'large' values of 2 does not. 1 + 2 = 4 For large values of 2 Because 2.99' can be thought of as 3, as its always drawing closer to 3, so 1 + 3 = 4 __________________ Spency. PIC Micro's - Your mind is the limit PIC's and interfacing with other devices - a PIC Basic Guide @ digital-diy.net

19th April 2007, 04:20 AM	(permalink)
dknguyen	0.999...~= 1? Yes! 0.999... = 1? No. End of story. If you do write down 1 in your calculations, it's because the difference is so small it doesn't matter (same reason why we round numbers). Last edited by dknguyen; 19th April 2007 at 06:37 PM.

19th April 2007, 11:14 AM	(permalink)
Pommie	And, as X approaches infinity then (1+1/X)^X approaches e. Mike.

19th April 2007, 02:34 PM	(permalink)
Pommie	The natural constant e is the amount in billions of dollars that google was valued at when it floated on the NYSE. It is also the base of natural logarithms. See wiki. In fact they define e as, Mike.