/sci/ - Science & Math

is this an ok proof for pic related (just the [math] a [/math] part obviously)
suppose [math] f(a)<\lambda [/math]. then take [math] \epsilon=\lambda-f(a) [/math]. since [math] f [/math] is continuous [math] |f(x)-f(a)|<\lambda-f(a) [/math], whenever [math] |x-a|<\delta [/math] and [math] x\in[a,b] [/math]. but then [math] f(x)<\lambda [/math] whenever [math] x\in[a,b] [/math], which is a contradiction.