Is 0.9999... Equal to 1? Debunking the Myth and Understanding the Concept

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In summary, the conversation discussed the concept of 0.99999... and whether it is equal to 1 or not. The speaker was initially shocked and lost belief in math as being absolute. The conversation also touched on the idea of whether 1.00 is equal to 1 or not. The speaker also mentioned a link for further reading on the topic. Ultimately, it was concluded that 0.99999... is equal to 1 and this has been discussed and proven many times. The question was raised about whether the speaker truly understands the concept of 0.99999... and the significance of asking if 1.00 is equal to 1.
  • #1
Raza
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At first, when I saw this, I was deeply shocked and lost the believe that math is absolute. Like the thinking that if Math can prove it, it must exist and if it can't, it doesn't exist.

So is 0.99999...=1 illogical?

also, is it fair to say that 1.00=1?

Sorry if this question is already posted or it's in the wrong forum.
 
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  • #3
0.99999(9) is 1
It's right and logical. Unfortunately, I don't remember the prove now, it was on the first grade in University.
 
  • #4
This has been slogged out many times: there's no need for another discussion thread.
 
  • #5
The real question, Raza, is do you know what 0.9999... means? If not, you certainly can't say that 0.9999...= 1 is an error! If you believe you do, what do you think 0.9999... means? The fact that you ask if 1.00= 1 makes me wonder.
 

FAQ: Is 0.9999... Equal to 1? Debunking the Myth and Understanding the Concept

Is 0.999 = 1 an error in math?

No, 0.999 does not equal 1 is not an error in math. In fact, 0.999 is a perfectly valid way of representing the number 1 in the decimal number system.

How is 0.999 equal to 1?

In the decimal number system, repeating the last digit in a decimal number signifies that the number continues infinitely. Therefore, 0.999 is equal to 0.99999999... which is essentially equal to 1.

Is there a mathematical proof for 0.999 = 1?

Yes, there are multiple mathematical proofs that show 0.999 is equal to 1. One example is using the formula for geometric series to show that 0.999 is equal to 1.

Are there real-life applications of 0.999 = 1?

Yes, the concept of 0.999 being equal to 1 is used in various fields such as mathematics, physics, and engineering. It is also used in everyday situations such as measurements and calculations.

Why is it important to understand that 0.999 = 1?

Understanding that 0.999 is equal to 1 is important as it helps in simplifying calculations and understanding mathematical concepts. It also allows for a better understanding of the concept of infinity and the decimal number system.

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