Number of Modules – A Little Theory of Groups (Group Theory is about something else)

a number of hardware and software modules…”

We have an “and”, and need to connect appropriately around it. Possible connections are:

anumber.png (54330 bytes)

We could use similarity to determine the most likely combination, but there is another influence – “number”.

number” can be singular or plural, depending on whether the count is referred, or the group, of which number is the count –

The number of accidents is increasing

A number of accidents have occurred

We could set up something similar to the mechanisms for “either … or …” or “between… and…”, in that “a number of” will search for a plural verb, bound the area, resolve it, and continue. This would give us

anumber1.png (45261 bytes)

This is not accurate, because we require a plural noun (or a noun that can be singular or plural, like “aircraft”), making the choice of (hardware and software) unequivocal.  What it does do is bound our test for similarity.

Sometimes we need to swallow multiple plural nouns into the group

A number of violent robberies and acts of terrorism have unsettled the city

Sometimes the “and” lies outside the group, forming a new group.

A number of violent robberies and an act of terrorism have unsettled the city.

Sometimes the “and” is another type.

The gang was accused of a number of violent robberies, and acts of terrorism have also unsettled the city.

So, “a number of” finds and groups plural nouns, unless there is a stronger competing claim. “number of” acts as a group generator, in the same way as “including” or specialised generators like “either” or “between”.

Other group generators –

Group of
Series of
Collection of
Fleet of
Assembly of
Team of
Consisting of
Comprising
Made up of

All of them are groups or relations that generate or operate on groups.

 Design Notes