#### Mathematical English Usage - a Dictionary

##### by Jerzy Trzeciak

## by

By continuity <By the continuity> of f,......

By assumption,......

By the above,......

By the induction hypothesis,......

By and large, we shall use the same notation as in......
[= In general]

term-by-term differentiation

a 3 by 4 matrix = a 3× 4 matrix

Thus we need only alter our constants by a factor of 2 to deal with this case.

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