Proof that every convergent sequence is bounded (ILIEKMATHPHYSICS)
This video references "Intro to Real Analysis" by Bartle and Sherbert Fourth Edition. For more details related to the context of this video, see section 3.2. The fact in this video is given by Theorem 3.2.2.
![lim(xn + yn) = lim(xn) + lim(yn) Proof [ILIEKMATHPHYSICS]](https://i.ytimg.com/vi/iKo3GX7W4Vs/hqdefault.jpg?sqp=-oaymwEjCNACELwBSFryq4qpAxUIARUAAAAAGAElAADIQj0AgKJDeAE=&rs=AOn4CLDqd_uZeZvz7L7moIpOwmTomny5Fg)
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lim(xn + yn) = lim(xn) + lim(yn) Proof [ILIEKMATHPHYSICS]
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Real Analysis | A convergent sequence is bounded.
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![If a sequence converges to x, then all of its subsequences converge to x (Proof) [ILIEKMATHPHYSICS]](https://i.ytimg.com/vi/vNI2eIUQWQg/hqdefault.jpg?sqp=-oaymwEjCNACELwBSFryq4qpAxUIARUAAAAAGAElAADIQj0AgKJDeAE=&rs=AOn4CLAZBU8sI8c6OPyj5LWhctnXI6zolw)
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If a sequence converges to x, then all of its subsequences converge to x (Proof) [ILIEKMATHPHYSICS]
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