Visual proof of if ∞=1/0, then 0=1/∞

In summary, the visual proof of the statement "if ∞=1/0, then 0=1/∞" involves graphing the function f(x) = 1/x and showing that as x approaches 0, the value of f(x) approaches infinity. This is a graphical representation of the mathematical statement ∞=1/0. However, this visual proof cannot be used as a substitute for a mathematical proof. Division by 0 is undefined in mathematics and the statement ∞=1/0 serves as a reminder to follow the rules of arithmetic when dealing with infinity.
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anemone
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A visual proof of the following statement:

If $\infty=\dfrac{1}{0}$, then $0=\dfrac{1}{\infty}$ .

Proof:

Assume $\infty=\dfrac{1}{0}$. Rotate each side of the equation counterclockwise $90^{\circ}$. We get 8 = −10. Subtract 8, getting 0 = −18. Then rotate both parts back: $0=\dfrac{1}{\infty}$. QED.
 
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  • #2
anemone said:
A visual proof of the following statement:

If $\infty=\dfrac{1}{0}$, then $0=\dfrac{1}{\infty}$ .

Proof:

Assume $\infty=\dfrac{1}{0}$. Rotate each side of the equation counterclockwise $90^{\circ}$. We get 8 = −10. Subtract 8, getting 0 = −18. Then rotate both parts back: $0=\dfrac{1}{\infty}$. QED.
I think this proof answers the question: "What did you divide by this time??"

-Dan
 

FAQ: Visual proof of if ∞=1/0, then 0=1/∞

1) What is the visual proof of the statement "if ∞=1/0, then 0=1/∞"?

The visual proof of this statement involves drawing a graph of the function f(x) = 1/x. As x approaches 0 from the positive side, the value of f(x) approaches positive infinity. Similarly, as x approaches 0 from the negative side, the value of f(x) approaches negative infinity. This graph shows that ∞=1/0, but it does not prove that 0=1/∞.

2) How does this visual proof relate to the mathematical statement ∞=1/0?

This visual proof is a graphical representation of the mathematical statement ∞=1/0. It shows that as x approaches 0, the value of 1/x approaches infinity, representing the concept of division by 0 resulting in infinity.

3) Can this visual proof be used as a substitute for a mathematical proof?

No, this visual proof is not a substitute for a mathematical proof. While it provides a visual representation of the statement, it does not provide a rigorous mathematical proof. In order to prove the statement, one must use mathematical principles and logic.

4) Is it possible to divide by 0 in mathematics?

No, it is not possible to divide by 0 in mathematics. Division by 0 is undefined and does not follow the rules of arithmetic. This is why the statement ∞=1/0 is not considered a valid mathematical statement.

5) What is the significance of this statement in mathematics?

The statement "if ∞=1/0, then 0=1/∞" is significant because it highlights the undefined nature of division by 0. It also serves as a reminder to be cautious when dealing with infinity and to always follow the rules of arithmetic in mathematical calculations.

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