Is 0=1 or is it my mistake? A question on indefinite integration.

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In summary, the mistake made was assuming that the constant of integration "c" must be the same in both integrals, when in reality it can be different. This is especially true in indefinite integration, where the constant in the right integral can cover for the addition of '1'. In definite integration, the boundaries need to be put on 1, resulting in 0 and no contradiction.
  • #1
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Obviously it is my mistake but i am wondering what is the mistake i made. First of all, i didn't know how to type math in this forum so i attached a word document with my "idea"
 

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  • #2
Your mistake lies in assuming that the constant of integration must be the same "c".
It won't be.
 
  • #3
arildno said:
Your mistake lies in assuming that the constant of integration must be the same "c".
It won't be.

could you explain a little more?
 
  • #4
nicksauce , i got an email that you replied but i can't see your post
 
  • #5
In an indefinite integration you will get a constant c. It doesn't have to be the same in b oth integrals so the constant in the right integral will cover for the addition of '1'.

In definite integration, you will need to put the boundaries on 1 to.
So it will be lie:

[tex]1_{x=b}-1_{x=a}[/tex]

Which is of course zero, and therefore there is no contradiction.
 
  • #6
elibj123, thank you very much I was referring to indefinite integration and i understand now. Again thanks
 

1. What does the equation "0=1" mean?

The equation "0=1" means that two numbers, 0 and 1, are equal to each other. This is a false statement, as 0 and 1 have different numerical values.

2. Is it possible for 0 to equal 1?

No, it is not possible for 0 to equal 1. In mathematics, 0 is defined as the absence of any quantity, while 1 is defined as the first whole number. These two numbers have distinct meanings and cannot be equal to each other.

3. Why is the equation "0=1" considered a contradiction?

The equation "0=1" is considered a contradiction because it violates the fundamental property of equality, which states that two quantities are equal if and only if they have the same value. Since 0 and 1 have different values, the equation cannot be true.

4. Can you give an example of a real-life situation where "0=1" could be true?

No, there are no real-life situations where "0=1" could be true. This equation goes against the basic principles of mathematics and contradicts real-world observations and experiences.

5. How does the concept of "0=1" relate to the idea of infinity?

The concept of "0=1" does not directly relate to the idea of infinity. However, both concepts are often used in mathematical equations and theories, and they both require careful understanding and application to avoid contradictions and errors.

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