# Dictionary Definition

strictly adv

1 restricted to something; "we talked strictly
business" [syn: purely]

2 in a stringent manner; "the laws are
stringently enforced"; "stringently controlled" [syn: stringently]

3 in a rigorous manner; "he had been trained
rigorously by the monks" [syn: rigorously]

# User Contributed Dictionary

## English

### Pronunciation

### Adverb

#### Related terms

# Extensive Definition

In mathematical writing, the
adjective strict is used to modify technical terms which have
multiple meanings. It indicates that the exclusive meaning of the
term is to be understood. (More formally, one could say that this
is the meaning which implies the other meanings.) The opposite is
non-strict. This is often implicit but can be put explicitly for
clarity.

This term is commonly used in the context of
inequalities
— the phrase "strictly less than" means "less than and
not equal to" (likewise "strictly greater than" means "greater than
and not equal to"). More generally a , strict
total order and strict
weak order exclude equality and equivalence.

A related use occurs when comparing numbers to
zero — "strictly positive" and "strictly negative" mean
"positive and not equal to zero" and "negative and not equal to
zero", respectively. Also, in the context of functions, the adverb
"strictly " is used to modify the terms "monotonic", "increasing",
and "decreasing".

On the other hand, sometimes one wants to specify
the inclusive meanings of terms. In the context of comparisons, one
can use the phrases "non-negative", "non-positive",
"non-increasing", and "non-decreasing" to make it clear that the
inclusive sense of the terms is intended.

Using such terminology helps avoid possible
ambiguity and confusion. For instance, upon reading the phrase "x
is positive", it is not immediately clear whether x = 0 is
possible, since some authors might use the term positive loosely,
and mean that x is not less than zero. Therefore, it is prudent to
write "x is strictly positive" for x>0 and "x is non-negative"
for x≥0. (A precise term like non-negative is never used
with the word negative in the wide, loose sense that includes
zero.)

The word "proper" is often used in the same way
as "strict." For example, a "proper
subset" of a set S is a subset that is not equal to S itself,
and a "proper
class" is a class which is not also a set.

strictly in German: Streng

# Synonyms, Antonyms and Related Words

absolutely, accurately, austerely, conscientiously,
dead, definitely, directly, even, exactingly, exactly, expressly, exquisitely, faithfully, fussily, grimly, harshly, in all respects, in
detail, in every respect, ipsissimis verbis, just, literally, literatim, meticulously, minutely, nicely, plumb, point-blank, positively, precisely, punctiliously, punctually, refinedly, right, rigidly, rigorously, ruggedly, scrupulously, severely, square, squarely, sternly, straight, stringently, to the letter,
toughly, undeviatingly, unerringly, verbally, verbatim, verbatim et
litteratim, with exactitude, with great nicety, with precision,
word by word, word for word