File:Bolzano–Weierstrass theorem - step 7.svg

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English: # A bounded sequence on the real number line with one of its lower bound and one of its upper bound .
  1. We take the first interval .
  2. Now we split the interval into twi equally sized subintervals.
  3. We take this subinterval for , which contains infinitely many members of
  4. Then we split again into two equally sized subintervals.
  5. We take this subinterval which contains infinitely many members of
  6. With continuing this process we get nested intervals. The point being in all those intervals is an accumulation point of .
Date
Source Own work
Author Stephan Kulla (User:Stephan Kulla)
Other versions
  • 1. step of Bolzano–Weierstrass theorem
    1. step of Bolzano–Weierstrass theorem
  • 2. step of Bolzano–Weierstrass theorem
    2. step of Bolzano–Weierstrass theorem
  • 3. step of Bolzano–Weierstrass theorem
    3. step of Bolzano–Weierstrass theorem
  • 4. step of Bolzano–Weierstrass theorem
    4. step of Bolzano–Weierstrass theorem
  • 5. step of Bolzano–Weierstrass theorem
    5. step of Bolzano–Weierstrass theorem
  • 6. step of Bolzano–Weierstrass theorem
    6. step of Bolzano–Weierstrass theorem
  • 7. step of Bolzano–Weierstrass theorem
    7. step of Bolzano–Weierstrass theorem
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