Vector Properties: Does Length Affect Components?

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The discussion centers on the mathematical limit of vector components as the vector length approaches zero, specifically examining the expression \lim_{||v||\to 0} \frac{v_i}{||v||}. Participants agree that as the length of a vector approaches zero, its components also approach zero. The conversation highlights the importance of understanding limits in vector calculus and the need for self-calculation in mathematical inquiries.

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nuuskur
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Is there something said about \lim_{||v||\to 0} \frac{v_i}{||v||}? Is it correct to assume if the length of a vector approaches 0, then any component of that vector has to approach 0, aswell?
 
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I would say yes... check out the proof I did... which I think works.. and similarily with substituting into y.
 

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DannyMoretz said:
I would say yes... check out the proof I did... which I think works.. and similarily with substituting into y.
It is against the rules at PF to give answers like that. You should've asked the OP to calculate the limits himself/herself.
 
I didn't post this in a homeworks' section and it isn't one, either. I was merely curious and couldn't find relevant info on it myself, since my English is bad.
 
nuuskur said:
I didn't post this in a homeworks' section and it isn't one, either. I was merely curious and couldn't find relevant info on it myself, since my English is bad.
Sorry, I didn't pay attention to the section. But I wanted to mention it to Danny, who is new here. It would still have been better to start by pointing you in the right direction.
 

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