Visual proof of if ∞=1/0, then 0=1/∞

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SUMMARY

The discussion presents a visual proof asserting that if ∞ equals 1/0, then 0 equals 1/∞. The proof involves a series of mathematical manipulations, including rotating the equation counterclockwise by 90 degrees, leading to the conclusion that 0 equals 1/∞. This unconventional approach highlights the paradoxical nature of infinity and division by zero, ultimately reinforcing the statement through visual representation.

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  • Understanding of mathematical concepts related to infinity and limits.
  • Familiarity with basic algebraic manipulation and rotation of equations.
  • Knowledge of the implications of dividing by zero in mathematics.
  • Basic understanding of visual proofs and their role in mathematical reasoning.
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  • Explore the concept of limits in calculus, particularly regarding infinity.
  • Study the implications of division by zero in different mathematical contexts.
  • Learn about visual proofs and their effectiveness in conveying complex mathematical ideas.
  • Investigate the properties of infinity in set theory and real analysis.
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Mathematicians, educators, and students interested in advanced mathematical concepts, particularly those exploring the nature of infinity and division by zero.

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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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
 

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