Question

let a belong to R show that the neighbourhood of absylum of a is a subset of the neighbourhood of 2 times the absylum of a for any absylum. Please

Answer 1

"absylum" = \(\epsilon\) ?

Answer 2

=]

Answer 3

Yes

Answer 4

I would think it's just a matter of applying the definition of a neighborhood on the real line.
\[\large N_\epsilon(a):=\{|a-x|<\epsilon~:~x\in\mathbb{R}\}\]
And to show \(\large N_\epsilon(a)\subseteq N_{2\epsilon}(a)\), you just have to show that
\[|a-x|<\epsilon\le2\epsilon\]
which doesn't look like much of a challenge. Something tells me it's more difficult than that...

Answer 5

It always seems simple in Intro to Analysis but than there is these little proofs and theorems we have to include in the answer. But thanks though, helped me understand the concept!