1 = 0

Sander Rossel

A high school teacher showed this to me some 10+ years back (feeling old now). All I can say is no.

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HobbyProggy

The only thing i can agree with is that 1 != 3/3 (at least not exactly) because 1/3 is 0,333... and multiplied with 3 it is just 0,99999.... which is technically 1 but not 100%

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CPallini

Quote:

Dividing by (x-y), obtain...

...the silent reproach of a million tear-stained eyes. :((

CPallini

Quote:

0,99999.... which is technically 1 but not 100%

Uh?

HobbyProggy

Whats the matter ?

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Rage

Dominic Burford wrote:

since we started with y nonzero.

oh, the irony.

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Nagy Vilmos

if the numerator and denominator are equal then the value must be 1. Then the second part is almost right, but you missed a very important point, a recurring value is only an *approximation* rather than the absolute. 1/3 is absolute, but the decimal 0.3. is only an approximation. Proof, without bad maths of the 9's reccuring - 0.9. == 1 Multiply by 10: 9.9. = 10 Subtract the original: 9.9. - 0.9. = 9 9 = 9 QED. This is accepted as proper maths, the 1=0 using division by zero is, however, not.

veni bibi saltavi

HobbyProggy

Nice :) But i guess as long as we have an approximation i'll go with its not exactly 1 :P

Nagy Vilmos wrote:

This is accepted as proper maths, the 1=0 using division by zero is, however, not.

I already said that in an other statement that hes wrong

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CPallini

0.9999... is 1.

HobbyProggy

By definition, not by maths :)

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Marc Clifton

Ah, the ol' divide by zero trick. I think my math teacher did that when I was in 8th grade. Almost 40 years ago. And I'm sure it's older than that. ;) Marc

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CPallini

By maths. There's no difference.

HobbyProggy

Allright, tell that the next flightcomputer that breakes down because he multiplied 0,333 and didn't get to 1 ;)

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CPallini

You know, float are not real numbers. (likewise Computer Science is not Mathematics) :-D

HobbyProggy

CPallini wrote:

(likewise Computer Science is not Mathematics)

But its both logic :) And 0,999 is not 1 it's even written different :sigh: But i guess we could debate ages about that

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CPallini

Right: we could follow all the nines until we find a difference. :laugh:

Richard Deeming

Take your pick: How Can 0.999... = 1? | Purplemath[^] For example:

  x = 0.999...

10x = 9.999...
10x - x = 9.000...
9x = 9
x = 1

EDIT: As Nagy said[^], 2+ hours ago.

"These people looked deep within my soul and assigned me a number based on the order in which I joined." - Homer

HobbyProggy

1/6 ->*6 0,966666666

x = 0,9666
10x = 9,6666
10x -x = 8,7066
9x = 8,7066
x = 0,9674

!

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HobbyProggy

1/6 = 0,166666 ->*6 0,9996

x = 0,9996
10x = 9,996
10x -x = 8,9964
9x = 8,9964
x = 0,9996

?

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Richard Deeming

HobbyProggy wrote:

1/6 = 0,166666 ->*6 0,9996

Nope - 6 × 0.1666... = 0.9999... It's simple multiplication:

1 x 6 = 6 (0.6)
6 x 6 = 36 = add 3 to the column on the left (6 + 3 = 9), and put 6 in this column (0.96)
6 x 6 = 36 = add 3 to the column on the left (6 + 3 = 9), and put 6 in this column (0.996)
6 x 6 = 36 = add 3 to the column on the left (6 + 3 = 9), and put 6 in this column (0.9996)
6 x 6 = 36 = add 3 to the column on the left (6 + 3 = 9), and put 6 in this column (0.99996)
etc.

Because you're repeating the operation an infinite number of times, there's no point where you stop and leave the last digit as 6. There's always another digit to the right which needs to be multiplied by 6, carrying the 3 into the current column.

"These people looked deep within my soul and assigned me a number based on the order in which I joined." - Homer