Does 0.999999.... equal 1?

[Barney_Gumble]

Some people say it does, other say no because a number needs to be whole.

Discuss.

 

[UFO Tatsu]

Two different numbers so No. If the question was "approximately equal" then that is a different story.

 

[Barney_Gumble]

Two different numbers so No. If the question was "approximately equal" then that is a different story.

Are you referring to real numbers?

 

[exe ex machina]

Fractions of numbers are not numbers.

 

[Barney_Gumble]

Fractions of numbers are not numbers.

Except in the case of real numbers, because the value represents a quantity along a continuous line. So technically 0.999..... does equal 1.

 

[Croweater]

No, it does not equal 1.

It would be like saying "I only lost that race by 0.001 of a second, therefore we were equal". Doesn't make much sense, does it?

 

[JoseMourinho]

Yes, if you round it up

 

[exe ex machina]

Except in the case of real numbers, because the value represents a quantity along a continuous line. So technically 0.999..... does equal 1.

No it isnt. Good example is if you multiply by a very large whole number you will see the difference more.

Example.
0.99 x 500 = 495
1.00 x 500 = 500

A whole FIVE numbers short of.

 

[Gough]

Been some pretty decent bank frauds carried out using this sort of idea, and shaving the fractions of cents off interest payments which all adds up very quickly.

 

[Barney_Gumble]

No, it does not equal 1.

It would be like saying "I only lost that race by 0.001 of a second, therefore we were equal". Doesn't make much sense, does it?

If we're talking about whole numbers, you're correct.

In terms of real numbers, then 0.999..... technically equals 1.

 

[Marklar_33]

Except in the case of real numbers, because the value represents a quantity along a continuous line. So technically 0.999..... does equal 1.

If we're talking about whole numbers, you're correct.

In terms of real numbers, then 0.999..... technically equals 1.

Why ask a question when you've decided the answer?

 

[Barney_Gumble]

Why ask a question when you've decided the answer?

Because the thread is a discussion on the topic. You're more than welcome to contribute your opinion.

 

[BALKAN]

Yes it does.

No it isnt. Good example is if you multiply by a very large whole number you will see the difference more.

Example.
0.99 x 500 = 495
1.00 x 500 = 500

A whole FIVE numbers short of.

The question isn't about a number with a finite number of decimal points but 0.999...recurring infinitely.

 

[Marklar_33]

Yes it does.



The question isn't about a number with a finite number of decimal points but 0.999...recurring infinitely.

The number becomes so close to 1 as to be indistinguishable from 1, but it will never be 1

 

[Barney_Gumble]

The number becomes so close to 1 as to be indistinguishable from 1, but it will never be 1

Here's an interesting thought:

We know that 0.9999... is not equal to 1. If you stop the expansion of 9s at any finite point, the fraction you have (like .99999 = 99999/100000) is never equal to 1. But each time you add a 9, the margin error is smaller (with each 9, the error is actually ten times smaller)

 

[Marklar_33]

Here's an interesting thought:

We know that 0.9999... is not equal to 1. If you stop the expansion of 9s at any finite point, the fraction you have (like .99999 = 99999/100000) is never equal to 1. But each time you add a 9, the margin error is smaller (with each 9, the error is actually ten times smaller)

mindblown.gif

 

[Barney_Gumble]

mindblown.gif

How about contributing something constructive to the thread instead of being a ******?

 

[Bunk Moreland]

No, it doesn’t. It equals 0.999999.

 

[Marklar_33]

How about contributing something constructive to the thread instead of being a ******?

I'll contribute constructively when you don't contribute at all

 

[Gough]

It's almost 1, same way Bradman's average is almost 100.

 

[Scotland]

No. 1 is an integer, 0.999999 is a fractional number.

In a discrete scenario, 0.999999 is irrelevant. You get 6 points for a goal and 1 for a behind. There is no such thing as a half goal or a quarter behind etc.

In a continuous scenario, whole numbers are irrelevant. There is no such thing as kicking from 50m. The 50m line at any point will be 50.001m or 49.999m etc. If you could measure down to fractions of a millimetre there is still no thing a 50m exactly. Just like there is no such thing as a 375mL beer. Each one is 375 mL +/- a tolerance and the practical difference between 375.001 and 374.999 isn't noticeable.

 

[IKnowtheDog]

Been some pretty decent bank frauds carried out using this sort of idea, and shaving the fractions of cents off interest payments which all adds up very quickly.

But it gets you a trip to a 'pound you in the a$$ prison' if caught

 

[rdhopkins2]

It's almost one, the same as VFA premierships aren't counted in footy.

Or a non eligible Grant for the Brownlow after a soft suspension.

Nearly but not quite.

 

[The Passenger]

There is a lot of debate in the mathematical world about whether 0.9.... = 1

A lot of it falls on the side that they are indeed equal.

EDIT:

It should be clarified the key to the question in a mathematical sense is the .... which refers to an infinite amount of decimals

The equation isn't 0.999999999 = 1, but rather 0.999999.... = 1

 

[Illinois Nazi]

If we are talking 0.9 recurring, then yes, it equals 1.