* Assume A is non-negative primitive matrix of size n, then A < sup > n < sup > 2 </ sup >- 2n + 2 </ sup > is positive.

Assume the square root of D is a rational number p / q, assume the q here is the smallest for which this is true, hence the smallest number for which q √ D is also an integer.

Assume now that the polynomial has a unitary root of multiplicity d. Then it can be rewritten as:

Assume it is true for all numbers less than n. If n is prime, there is nothing more to prove.

Assume D is a non-square natural number, then there is a number n such that:

Assume that p − 1, where p is the smallest prime factor of n, can be modelled as a random number of size less than √ n.

Assume G is some graph and is some path of length n on G. In other words, are vertices of G such that and are neighbors.

* Assume n

* Assume n > 0.

The setting is as follows: Assume that k is a field and let K be a subfield of the field of rational functions in n variables,

Assume that for all n,.

Assume that these two lines are each incident to n points.

Assume further that the coordinate systems are oriented so that, in 3 dimensions, the x-axis and the x ' - axis are collinear, the y-axis is parallel to the y ' - axis, and the z-axis parallel to the z ' - axis.

Assume p and q − 1 are relatively prime, a similar application of Fermat's Little Theorem says that ( q − 1 )< sup >( p − 1 )</ sup > ≡ 1 ( mod p ).

Assume that we are given some integers, such as

Assume parts of a maximally entangled Bell state are distributed to Alice and Bob.

Assume there are a group of N atoms, each of which is capable of being in one of two energy states, either

Assume the wire costs are the same by weight.

Assume now that a and b are not necessarily equal vectors, but that they may have different magnitudes and directions.

Assume that the limit superior and limit inferior are real numbers ( so, not infinite ).

** Assume that there are two consumption bundles A and B each containing two commodities x and y.

: Assume an Ethernet broadcast domain ( e. g., a group of stations connected to the same hub ) using a certain IPv4 address range ( e. g., 192. 168. 0. 0 / 24, where 192. 168. 0. 1 – 192. 168. 0. 127 are assigned to wired nodes ).

Assume a uniform prior of, and that trials are independent and identically distributed.

Assume that the channel from A to B is initialized and that there are no messages in transit.

Assume there are no external costs, so that social cost equals individual cost.

Assume a hand is dealt and that spades are named as trump.

Assume two matrices are to be multiplied ( the generalization to any number is discussed below ).

Assume without loss of generality that A and B are disjoint.

Assume we notice that there are on average 2 customers in the queue and at the counter.

Assume that there exists a basis for such that and are all approximately orthogonal to a good degree if i is not j and the same thing for and and also and for any i and j ( the decoherence property ).

Assume a hunters ’ economy with free land, no slavery and no significant current production of tools, where beavers and deer are hunted.

Assume that the available data ( y < sub > i </ sub >, x < sub > i </ sub >) are mismeasured observations of the “ true ” values ( y < sub > i </ sub >*, x < sub > i </ sub >*):

Assume there are four agents: two use the tit-for-tat strategy, and two are " defectors " who will simply try to maximize their own winnings by always giving evidence against the other.

Consider a polygon P and a triangle T, with one edge in common with P. Assume Pick's theorem is true for both P and T separately ; we want to show that it is also true to the polygon PT obtained by adding T to P. Since P and T share an edge, all the boundary points along the edge in common are merged to interior points, except for the two endpoints of the edge, which are merged to boundary points.

Assume the Earth is in L, at the second quadrature with Jupiter ( i. e. ALB is 90 °), and Io emerges from D. After several orbits of Io, at 42. 5 hours per orbit, the Earth is in K. Rømer reasoned that if light is not propagated instantaneously, the additional time it takes to reach K, that he reckoned about 3½ minutes, would explain the observed delay.

Assume also that the phase can be measured with an accuracy of 1 deg, i. e. means that the range can be determined with a precision of ( 600000 * 1 * Pi )/( 2 * 8000 * 180 )= 0. 33 km.

Let V < sup > i </ sup > be the subspace of V on which L < sub > 0 </ sub > has eigenvalue i. Assume that V is acted on by a group G which preserves all of its structure.

Assume random variables are i. i. d.

Assume that bidder i bids.

Assume this happens at J i. e. is the last.

Assume that, i. e. that the posterior distribution factorizes into independent factors for and.

Assume k is a fixpoint and k < m. Than there has to be i such that.

Assume that the time required for goal passing ( i. e. passing a pointer through a goal at distance A and of width W,

( Assume for simplicity that she cares only about her monetary earnings, and that she values earnings at different times equally, i. e., the discount rate is zero.