Is 1 Really Equal to .9999999999999999999?

  • Thread starter Demodocus
  • Start date
In summary, there is a well-known mathematical concept called "convergence" that explains why 0.9999... is equal to 1. This may seem like a paradox, but it simply means that our definition of infinity needs to be refined. This topic has been discussed and debated extensively by mathematicians.
  • #1
Demodocus
7
0
1= .9999999999999999999...

Here it is...

1/3= .33333333333...

2/3= .6666666666...

so

3/3= .9999999999...

so

1= .999999999...

Wtf?

I think that this "paradox" means that there is a problem with our definition of infinity. At least, the definition needs to be refined. Does this mean that 1 is not equal to one, or is .9999999... another name for one? I think this topic needs to be adressed.
 
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  • #2
Oh no, I remember a long one discussing this. Something about convergence, but I'll sit back and watch :)
 
  • #4
Ouch! Another one. Demodocus- there is nothing wrong with "our" definition of infinity (actually, I can't speak for yours). Yes, 0.9999... is just another name for 1 (that, I must say, is put very nicely). Our definition of "base 10 enumeration system" is such that 0.9999... means the sum of the infinite series 9/10+ 9/100+ 9/100+ ... which is a geometric series that can be shown to converge to 1.
 

What is 1= .9999999999999999999.?

1= .9999999999999999999. is a mathematical equation that represents the concept of approaching but not quite reaching 1. It is often referred to as the "limit" of a sequence of numbers.

How is it possible for 1 to equal .9999999999999999999?

In mathematics, numbers can be represented in different forms, including decimal and fraction. While 1 is a whole number, .9999999999999999999 is a repeating decimal that is infinitely close to 1. Therefore, while they may look different, they are considered equivalent in mathematical terms.

Is .9999999999999999999 the same as 1?

Yes, as mentioned before, .9999999999999999999 and 1 are considered equivalent in mathematical terms. They may look different, but they represent the same value.

Why does this concept seem counterintuitive?

For many people, the idea of something being infinitely close but not quite equal to another number can be difficult to grasp. However, in mathematics, there are many concepts and principles that may seem counterintuitive at first but can be proven through mathematical reasoning and evidence.

How is this concept used in real life?

The concept of 1= .9999999999999999999 is often used in calculus and other advanced mathematical fields to represent limits and infinitesimal values. It also has applications in physics and engineering, where precise measurements and calculations are necessary.

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