Is 1 divided by infinity equal to zero?

  • Context: High School 
  • Thread starter Thread starter Nick666
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SUMMARY

The discussion centers on the question of whether 1 divided by infinity equals zero. Participants clarify that while the expression 1/∞ is not a valid computation in traditional mathematics, it can be interpreted in the context of limits. Specifically, the limit notation \lim_{x\to\infty} \frac{1}{x} = 0 is established as a valid mathematical concept. The conversation also touches on the philosophical implications of infinity and the nature of mathematical symbols, emphasizing that infinity itself does not represent a number in the conventional sense.

PREREQUISITES
  • Understanding of limits in calculus, specifically \lim_{x\to\infty}.
  • Familiarity with the concept of infinity in mathematics.
  • Basic knowledge of rational and irrational numbers.
  • Awareness of mathematical notation and its interpretations.
NEXT STEPS
  • Study the concept of limits in calculus, focusing on \lim_{x\to\infty} \frac{1}{x}.
  • Explore the extended real number system and its implications for infinity.
  • Research nonstandard analysis and its treatment of infinite quantities.
  • Investigate the philosophical aspects of infinity and its role in mathematics.
USEFUL FOR

Students of mathematics, educators, philosophers interested in mathematical concepts, and anyone seeking to understand the implications of infinity in mathematical discourse.

  • #31
matt grime said:
I want to cry.

Don't cry Matt. :biggrin:
 
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  • #32
cheer up matt, at least this isn't another 1/0 = 0 thread
 

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