0.99999... != 1

piranha · Post by **piranha** » Sat May 19, 2007 12:11 am

ok........the answer is 0.99999... != 1.

simple.

if it were the same, then it would be written the same.

alright...............so....same thing, different numbers:
0.3333...... and 0.4
0.3333..... == 3/9 or 1/3. 0.4 is not 1/3. 0.4 is 2/5.
now....
make fractions...set them equal...cross multiply...... and you get: 30 = 36. that doesn't work. so, no. 0.9999... and 1 are not equal

Tyler · Post by **Tyler** » Sat May 19, 2007 5:02 am

piranha wrote:ok........the answer is 0.99999... != 1.

simple.

if it were the same, then it would be written the same.

alright...............so....same thing, different numbers:
0.3333...... and 0.4
0.3333..... == 3/9 or 1/3. 0.4 is not 1/3. 0.4 is 2/5.
now....
make fractions...set them equal...cross multiply...... and you get: 30 = 36. that doesn't work. so, no. 0.9999... and 1 are not equal

Imbesile... go get a Degree in Maths and then attempt to discuss it when you learn that it is accepted that 0.99... is equal to 1. For the record there is not an infinetly small different between 0.33... and 0.4 obviously.

Zekrazey1 · Post by **Zekrazey1** » Sat May 19, 2007 6:41 am

'Imbecile'

Tyler · Post by **Tyler** » Sat May 19, 2007 4:49 pm

Yeah i never said i wasn't also an idiot...

anon19287473 · Post by **anon19287473** » Sun May 20, 2007 8:11 pm

I maintain that it does not equal one, it WOULD equal 0.0(repeated)1, except that this cannot exist, becuase the 1 would never be reached, the zero's go forever.

So i propose an imaginary number to represent 1-0.99999999999....., it will be a 'w' with a big swoosh at the end! Who's with me?!

A simple explanation... (*partially joking*)

'a' != 'b'
1 != 2
1.9 != 2
'a' != 2
'a' == 'a'
0.99999 != 1
1 == 1
0.9999 == 0.9999

THEY'RE BOTH DIFFERENT CONSTANTS..... THEY CANNOT BE EQUAL!!!!!

Solar · Post by **Solar** » Mon May 21, 2007 1:06 am

"Unfortunately", the links quoted in this thread indicate otherwise.

jnc100 · Post by **jnc100** » Mon May 21, 2007 7:12 am

This argument has probably been posted before but I can't be bothered to go back through the post to check:

If two numbers are different then there has to be a number between them.

Can anyone suggest a number between 0.999999.... and 1?

Thought not.

Tyler · Post by **Tyler** » Mon May 21, 2007 7:28 am

jnc100 wrote:This argument has probably been posted before but I can't be bothered to go back through the post to check:

If two numbers are different then there has to be a number between them.

Can anyone suggest a number between 0.999999.... and 1?

Thought not.

Yeah you don't even need Degree level maths... why not go to school and learn some simple maths like calculus?

Zekrazey1 · Post by **Zekrazey1** » Mon May 21, 2007 8:04 am

jnc100 wrote:This argument has probably been posted before but I can't be bothered to go back through the post to check:

If two numbers are different then there has to be a number between them.

Can anyone suggest a number between 0.999999.... and 1?

Thought not.

What's between the numbers 1 and 2 in the set of integers?

.

jnc100 · Post by **jnc100** » Mon May 21, 2007 9:02 am

Sorry, should have specified real numbers.

Actually, for some number systems then there is a difference between 0.999... and 1 (see Wikipedia article cited above).

Regards,
John.

Zekrazey1 · Post by **Zekrazey1** » Mon May 21, 2007 9:07 am

Ya, I was just being cheeky

.

os64dev · Post by **os64dev** » Tue May 22, 2007 1:01 am

I thought this i a general known issue:

in mathmatics 0.9999999.. != 1 and in computerscience 0.9999999.. == 1.

mainly because of a design flaw of the floating point unit.

hence the conditional checks for small deltas

Code: Select all

#define DELTA  0.0000000001 // or something similar small
if(((f1 -f2) < DELTA) || ((f1 -f2) < -DELTA)) {
    //- floats are near enough
}

Brendan · Post by **Brendan** » Tue May 22, 2007 3:42 am

Hi,

os64dev wrote:in mathmatics 0.9999999.. != 1

No.

0.9999999.. == 1

It's easy to prove too:

1 == 1
1 == 3/3
1 == 3 * (1/3)
1 == 3 * (0.3333...)
1 == 0.999...

os64dev wrote:and in computerscience 0.9999999.. == 1.

mainly because of a design flaw of the floating point unit.

hence the conditional checks for small deltas

The checks for small deltas are needed because of lack of precision, which in turn is caused by a finite number of bits used to store the significand. It's not a "flaw" in the design of the floating point unit (and SSE) - it's just a natural/unavoidable consequence of trying to store large things in small places.

The most common problem is that CPUs work in binary and some decimal numbers can't be represented precisely in binary. For example, "0.1" in binary repeats forever (it becomes 0.0001100110011001100110011...), so the CPU will either truncate it or round it to make it fit. This means that "(1 / 10) * 10" might give the answer 1.00000000000001 because the intermediate value "1 / 10" can't be represented precisely.

In the same way, for "(1 / 3) * 3" the CPU might calculate "1 / 3" as 0.33333333333 (not recurring) and then decide that the final answer is 0.99999999 (also not recurring), which is wrong because of precision loss. If the multiplication was done first then the CPU would give the correct answer (you could even get the correct answer using integers in this case).

Cheers,

Brendan

AJ · Post by AJ » Tue May 22, 2007 3:55 am

Code: Select all

a = b
a2 = ab
a2 - b2 = ab-b2
(a-b)(a+b) = b(a-b)
a+b = b
b+b = b
2b = b
2 = 1

I'm sure that most of you have seen this before - spot the mistake

Combuster · Post by **Combuster** » Tue May 22, 2007 4:14 am

AJ wrote:

Code: Select all

a = b
a2 = ab
a2 - b2 = ab-b2
(a-b)(a+b) = b(a-b)
a+b = b
b+b = b
2b = b
2 = 1

Thanks for reminding me to put that on some public blackboard.