- #1
c.teixeira
- 42
- 0
Hi comrades.
According to spivak, the defition of limit goes as follows:
" For every ε > 0, there is some δ > 0, such that, for every x, if 0 < |x-a| < δ,
then |f(x) - l |< ε. "
After some exercices, I came across with a doubt.
Say that I could prove that | f(x) - l |< 5ε, for some δ[itex]_{1}[/itex] such that 0 < |x-a| < δ[itex]_{1}[/itex].
Since ε > 0, and thus 5ε > 0, could I say that lim[itex]_{x→a}[/itex]f(x) = l based on this proof?
Regards,
According to spivak, the defition of limit goes as follows:
" For every ε > 0, there is some δ > 0, such that, for every x, if 0 < |x-a| < δ,
then |f(x) - l |< ε. "
After some exercices, I came across with a doubt.
Say that I could prove that | f(x) - l |< 5ε, for some δ[itex]_{1}[/itex] such that 0 < |x-a| < δ[itex]_{1}[/itex].
Since ε > 0, and thus 5ε > 0, could I say that lim[itex]_{x→a}[/itex]f(x) = l based on this proof?
Regards,