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Limit of Error function Erf


Dear group

I dont understand the following behaviour of Mathematica,
I would say the first result is simply wrong

1.)

Limit[Erf[1\/Sqrt[\[Alpha]\ t]], t -> \[Infinity],
    Assumptions -> {\[Alpha] > 0}]

gives infinity

2.)

Limit[Erf[1\/Sqrt[\[Alpha]\ t]], t -> \[Infinity],
    Assumptions -> {\[Alpha] == 1}]

gives zero

Any suggestions? Is this a bug?
Bye
Ben



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