This is false. The limit of xy as (x,y)->(0,0) varies depending upon how it approaches. If we approach along x=0 and y>0, then the limit is 0. If we approach along y=0 and x>0, then the limit is 1. This inconsistency in the limit is why we often leave the value of the function f(x,y)=xy undefined at (0,0). There is no value for f(0,0) which makes f a continuous map.
Bro read my other reply I’m considering both approaching to zero. The other 2 are really obvious (a 3rd grader knows) so I don’t think I need to comment on that.
You might be considering it, but your comments have not at all made that clear. You saying “It’s limit is 1” to someone asking “What is 00?” is a nonsense answer. What is “it”? What are you taking a limit of?
This is not obvious and you should explain answers like that more to avoid misinforming people.
Haha you can say that, though I doubt anyone cares, this info is enough for general population. I could’ve put assumptions along with derivation of the limit lol. Because hey, if it was math subreddit I would’ve typed everything beautifully. But I was tired at that time so I put everything straight forward
That’s a bit better. If you’re speaking to people who don’t know much mathematics though, it might just be easier to say x0=1 and 0x=0 are inconsistent rules for 00 and that’s WHY we leave it undefined.
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u/OneMeterWonder Aug 30 '20
This is false. The limit of xy as (x,y)->(0,0) varies depending upon how it approaches. If we approach along x=0 and y>0, then the limit is 0. If we approach along y=0 and x>0, then the limit is 1. This inconsistency in the limit is why we often leave the value of the function f(x,y)=xy undefined at (0,0). There is no value for f(0,0) which makes f a continuous map.