# Correct use of bound/bounded

I am not sure how to correctly use the word bound in this context:

All partial sums of two given sequences are bounded by a positive constant.

All partial sums of two given sequences are bound by a positive constant.

• 'Bounded' has a different meaning to 'bound'. The former has to do with boundary, indicating the limits of something. 'Bound' is the past tense of 'bind'. I am not sure if this helps, but you may need a dictionary of mathematical terms.
– WS2
Apr 8, 2014 at 8:03
• Yes, It seems that it is what I was looking for. Thanks. Apr 8, 2014 at 8:05

Verb: bind
Past: bound
Noun: a binding (in some senses)
Used in various senses in physics and computer science but not in mathematics.

Verb: bound
Past: bounded
Noun: a bound
Used in mathematics and computing to denote a range or finite area in which a value must be.

The sentence in your question is about a bound, therefore the past participle is bounded.

All partial sums of two given sequences are bounded by a positive constant.
There is a bound on the partial sums of two given sequences.

The difficulty you are facing is that there are two separate verbs in play here.

The verb bind means

Tie or fasten (something) tightly

Its past tense and past participle is bound

The verb bound (present tense) means

Form the boundary of; enclose

or

Place within certain limits; restrict

Bound can also mean

to move with a leap or series of leaps

In each of these cases, the past and past participle form of bound is bounded.

In the example given by the OP, it seems that the meaning is to place within limits (rather than to tie to). The verb would then be bound and the past participle is bounded. In the construction given, bounded is correct and bound is not.

The expression "to be bounded" meaning being limited or having a border is registered in English dictionaries.