Vector Properties: Does Length Affect Components?

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The discussion centers on whether the limit of a vector's components approaches zero as the vector's length approaches zero. Participants agree that if a vector's length tends to zero, its components should also approach zero. There is a mention of a proof supporting this claim, although the validity of the proof is not fully explored. One user emphasizes the importance of encouraging others to calculate limits independently rather than providing direct answers. The conversation highlights a mix of curiosity about vector properties and the importance of adhering to forum rules.
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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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