Is 1 divided by infinity equal to zero?

  • Context: High School 
  • Thread starter Thread starter Nick666
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Discussion Overview

The discussion revolves around the question of whether 1 divided by infinity is equal to zero. Participants explore various perspectives on this concept, touching on mathematical definitions, philosophical implications, and the use of limits in calculus.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Mathematical reasoning
  • Meta-discussion

Main Points Raised

  • Some participants suggest that in certain contexts, such as engineering or physics, 1 divided by infinity can be considered as approaching zero.
  • Others argue that the expression 1/infinity is not valid without the context of limits, specifically stating that the limit of 1/x as x approaches infinity equals zero.
  • A participant mentions that in the extended complex plane, 1/oo can be interpreted as zero, but cautions that the symbol does not have a universally accepted meaning.
  • There is a discussion about the nature of infinity and its representation, with some participants questioning the validity of using symbols like 999... to represent infinity.
  • Concerns are raised about misconceptions regarding the addition of natural numbers and the nature of infinite sums, with some participants asserting that adding an infinite number of natural numbers does not necessarily yield a natural number.
  • One participant highlights the distinction between finite and infinite sets, noting that while finite sets have maximum values, infinite sets may not, leading to different mathematical phenomena.

Areas of Agreement / Disagreement

Participants express a range of views on the topic, with no clear consensus reached. Some agree on the use of limits in defining the relationship between 1 and infinity, while others challenge the validity of such definitions and the meaning of infinity itself.

Contextual Notes

Limitations include the ambiguity surrounding the symbol for infinity and the varying interpretations of mathematical concepts related to limits and infinite sums. The discussion also reflects differing perspectives between mathematicians and those from engineering or philosophical backgrounds.

  • #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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