What could prove this wrong? I'm having a dispute with friends

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SUMMARY

The discussion centers on the concept of infinity in mathematics, specifically its application in calculus and number theory. Participants debate whether infinity can be treated as a number and how its context-dependent nature complicates its understanding. Key points include the distinction between countable and uncountable infinities, the use of limits, and the philosophical implications of infinity. The consensus is that while infinity is a useful mathematical concept, it remains complex and often misunderstood.

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  • Understanding of limits in calculus
  • Familiarity with countable and uncountable sets
  • Knowledge of Peano's axioms in number theory
  • Basic principles of mathematical notation and context sensitivity
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  • Study the concept of limits in calculus, focusing on epsilon-delta definitions
  • Explore the differences between countable and uncountable infinities, particularly through Cantor's theorem
  • Learn about the implications of Peano's axioms in defining natural numbers
  • Investigate the role of infinity in various mathematical contexts, such as set theory and calculus
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Mathematicians, educators, students in advanced mathematics, and anyone interested in the philosophical implications of mathematical concepts.

  • #91
Gavran said:
What about using a microscope?
That raises the question, what does ##\pi## look like under a microscope?
 
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  • #92
BWV said:
Is that what you saw of my post?
No. That's the 0.1% of the pixels in your post 84 I would have had to notice, in order to get the joke.

'Subtle' is an understatement. ;)
 
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  • #93
PeroK said:
That raises the question, what does π look like under a microscope?
It looks like a circle with a diameter of 1. The same can not be said for the figure in the original post.
 
  • #94
ducknumerouno said:
TL;DR Summary: Pi = 4?
I know it theoretically never touches the circle, but does the circle ever really become a circle?

problem-webp.webp


This iterative approximation reduces the area-error in each step, but it doesn't reduce the perimeter-error at all. So, it can used to derive the area of the circle but not its circumference (and pi from it).

See also this video:

 
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  • #95
Old thread but it dives up as a hot thread every time . I just want to say that there are several definitions of arc length. Math begins from definitions.
 
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