Does 0.999999.... equal 1?

[Jobe Watson]

Yes, yes it does.

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.

 

[ioppolo]

I rate this thread 9.999/10

 

[Big Cox 88]

There are 0.99999... 0 types of people in the world, those who read binary and those who don't.

 

[Marklar_33]

I rate this thread 9.999/10

Perfect score!

 

[kickazz]

Fractions of numbers are not numbers.

Of course they ****ing are numbers.

 

[exe ex machina]

Of course they ******* are numbers.

Is 3/5ths a number?

 

[kickazz]

x = 0.99999 ........
10x = 9.9999 ....... *10 both sides
10x = 9 + 0.99999 ........
10x = 9 + x
10x - x = 9
9x = 9
x = 1

1 = 0.99999 .......

 

[kickazz]

Is 3/5ths a number?

Yes

 

[exe ex machina]

Yes

Incorrect.

There are only 10 numerical digits. 0,1,2,3,4,5,6,7,8,9
There are WHOLE numbers (ie, numbers) that range from zero to trillions and trillions.
Fractions of numbers USE numerical digits (0-9) but the decimal place in itself means they are fractions of numbers not numbers as such.

1.5 is not A number. It is a description of a state of existence between two whole numbers otherwise referred to as a fraction of a number.
It being neither 1 nor 2. But a fraction of.

 

[kickazz]

Incorrect.

There are only 10 numerical digits. 0,1,2,3,4,5,6,7,8,9
There are WHOLE numbers (ie, numbers) that range from zero to trillions and trillions.
Fractions of numbers USE numerical digits (0-9) but the decimal place in itself means they are fractions of numbers not numbers as such.

1.5 is not A number. It is a description of a state of existence between two whole numbers otherwise referred to as a fraction of a number.
It being neither 1 nor 2. But a fraction of.

You don't know what you're talking about.

Whole numbers from 0 to trillions and trillions, and their negative counterparts, are integers which are a subset of rational numbers, which in turn are a subset of real numbers, which is a subset of numbers.

Then there are imaginary and complex numbers too, but that's starting to get technical.

Fractions are rational numbers, and therefore, numbers.

 

[exe ex machina]

You don't know what you're talking about.

Whole numbers from 0 to trillions and trillions, and their negative counterparts, are integers which are a subset of rational numbers, which in turn are a subset of real numbers, which is a subset of numbers.

Then there are imaginary and complex numbers too, but that's starting to get technical.

Fractions are rational numbers, and therefore, numbers.

They are mere DESCRIPTIONS of states of numerical value. Hence, terms like imaginary, complex, rational, etc.
Number in the strictest sense is a whole number.
Just like there are concepts like Pi, etc, they are not a number as such. Just mathematical devices, arguments, and descriptions of values.

 

[SwampCreature]

Guys, numbers are a human construct. None of them are real. It's made up.

 

[exe ex machina]

Guys, numbers are a human construct. None of them are real. It's made up.

So is Time

 

[SwampCreature]

No arguments here.

 

[Procrastinator35]

Guys, numbers are a human construct. None of them are real. It's made up.

That answer does not compute.

 

[Bunk Moreland]

Incorrect.

There are only 10 numerical digits. 0,1,2,3,4,5,6,7,8,9
There are WHOLE numbers (ie, numbers) that range from zero to trillions and trillions.
Fractions of numbers USE numerical digits (0-9) but the decimal place in itself means they are fractions of numbers not numbers as such.

1.5 is not A number. It is a description of a state of existence between two whole numbers otherwise referred to as a fraction of a number.
It being neither 1 nor 2. But a fraction of.

They're rational numbers.

You're being irrational.

 

[Good_Old]

Mainly on Tuesdays.

 

[flashmanvc]

One (is the loneliest number).

FACT!

 

[treefingers]

x = 0.99999 ........
10x = 9.9999 ....... *10 both sides
10x = 9 + 0.99999 ........
10x = 9 + x
10x - x = 9
9x = 9
x = 1

1 = 0.99999 .......

Came in here to post the exact same thing.

Another way of thinking about it is this -

1/3 = 0.3333333333*
2/3 = 0.6666666666*
3/3 =0.999999999999* = 1

*reoccuring

 

[Demosthenes]

It depends what you mean by 'equal'. All the question really demonstrates is the inability of mathematics as a system to deal with the concept of infinity.

The most correct thing to say would be 0.9 repeating approaches 1.

 

[exe ex machina]

It depends what you mean by 'equal'. All the question really demonstrates is the inability of mathematics as a system to deal with the concept of infinity.

The most correct thing to say would be 0.9 repeating approaches 1.

THANK-YOU.

 

[Norwegian Blue]

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

No there's not. Euler showed they were equal by expressing the LHS as a geometric progression. There's no debate whatsoever. Not in the mathematical world anyway.

This only ever comes up because it's counter intuitive.

 

[Sir James Sober]

Say there is a line from A to B

If you move in the direction of point A to point B and cover half the distance each time, you never get to B because it is always possible to divide any number by 2.

You never get to B and the distance gained is 0.99999 ........

 

[exe ex machina]

****ng nerds

 

[Walt Kowalski]

Say there is a line from A to B

If you move in the direction of point A to point B and cover half the distance each time, you never get to B because it is always possible to divide any number by 2.

You never get to B and the distance gained is 0.99999 ........

you'd get to B though, cos you'd trip over yourself trying to move such a small distance