and I asked myself a question: Suppose I had the same number of peas as there are atoms in my body, how large an area would they cover??

Suppose that in a mathematical language L, it is possible to enumerate all of the defined numbers in L. Let this enumeration be defined by the function G: W → R, where G ( n ) is the real number described by the nth description in the sequence.

Suppose v, e, and f are the number of vertices, edges, and regions.

It is frequently stated in the following equivalent form: Suppose that is continuous and that u is a real number satisfying or Then for some c ∈ b, f ( c ) = u.

Suppose a number of scientists are assessing the probability of a certain outcome ( which we shall call ' success ') in experimental trials.

Suppose that the distribution consists of a number of discrete probability masses p < sub > k </ sub >( θ ) and a density f ( x | θ ), where the sum of all the ps added to the integral of f is always one.

Suppose we used the negative binomial distribution to model the number of days a certain machine works before it breaks down.

Suppose you had a list of unique identifiers for each person in the room, like a social security number in the United States.

Suppose that for every real number x.

Suppose K is a number field ( a finite-dimensional field extension of the rationals Q ) with ring of integers O < sub > K </ sub > ( this ring is the integral closure of the integers Z in K ).

Suppose we have a container with a huge number of very small particles all with exactly the same physical characteristics ( mass, charge, etc .).

Suppose we have a number of energy levels, labeled by index

Suppose that we are sending messages through the channel with index ranging from to, the number of distinct possible messages.

Suppose we can use some number, to index the quality of used cars, where is uniformly distributed over the interval.

Suppose that the interval is split up in subintervals, with an even number.

Suppose it is necessary to know the price of the oil at 12: 00PM on one particular day in the past ; one must base the estimate on any number of samples that were obtained on the days before and after the event.

Suppose that f is entire and | f ( z )| is less than or equal to M | z |, for M a positive real number.

Suppose the number of a man's sons to be a random variable distributed on the set

Suppose that A is a set with a function w: A → N assigning a weight to each of the elements of A, and suppose additionally that the fibre over any natural number under that weight is a finite set.

) Suppose additionally that a < sub > n </ sub > is the number of elements of A with weight n. Then we define the formal Dirichlet generating series for A with respect to w as follows:

Suppose contains independent random components, each of which has three possible realizations ( for example, future realizations of each random parameters are classified as low, medium and high ), then the total number of scenarios is.

Suppose the total number of scenarios is very large or even infinite.

It is known that no non-constant polynomial function P ( n ) with integer coefficients exists that evaluates to a prime number for all integers n. The proof is: Suppose such a polynomial existed.

Suppose K is a Galois extension of the rational number field Q, and P ( t ) a monic integer polynomial such that K is a splitting field of P. It makes sense to factorise P modulo a prime number p. Its ' splitting type ' is the list of degrees of irreducible factors of P mod p, i. e. P factorizes in some fashion over the prime field F < sub > p </ sub >.

Suppose that the signal to be sent ( called the modulating or message signal ) is and the carrier onto which the signal is to be modulated is

:" Moses said to God, ' Suppose I go to the Israelites and say to them, " The God of your fathers has sent me to you ," and they ask me, ‘ What is his name ?’ Then what shall I tell them ?” God said to Moses, “ I AM WHO I AM " — Exodus 3: 13-14 ( New International Version ) ( see Tetragrammaton ).

) Then X < sub > i </ sub > is the value ( or realization ) produced by a given run of the process at time i. Suppose that the process is further known to have defined values for mean μ < sub > i </ sub > and variance σ < sub > i </ sub >< sup > 2 </ sup > for all times i. Then the definition of the autocorrelation between times s and t is

; Dennett's reply from natural selection: Suppose that, by some mutation, a human being is born that does not have Searle's " causal properties " but nevertheless acts exactly like a human being.

Unicity: Suppose satisfies, then by Theorem 1. 8,.

Suppose A is a n by n Invertible matrix.

* Suppose G and H are topologically finitely-generated profinite groups which are isomorphic as discrete groups by an isomorphism ι.

:: “ Suppose that a sheriff were faced with the choice either of framing a Negro for a rape that had aroused hostility to the Negroes ( a particular Negro generally being believed to be guilty but whom the sheriff knows not to be guilty )— and thus preventing serious anti-Negro riots which would probably lead to some loss of life and increased hatred of each other by whites and Negroes — or of hunting for the guilty person and thereby allowing the anti-Negro riots to occur, while doing the best he can to combat them.

An uncountable subset of the real numbers with the standard ordering ≤ cannot be a well-order: Suppose X is a subset of R well-ordered by ≤.

* Driving Like Crazy: Thirty Years of Vehicular Hell-bending Celebrating America the Way It's Suppose to Be – With an Oil Well in Every Backyard, a Cadillac Escalade in Every Carport, and the Chairman of the Federal Reserve Mowing Our Lawn ( 2010 ) Reprint edition by Grove Press ISBN 0802144799

Suppose that we have already constructed Lebesgue measure on the real line: denote this measure space by ( R, B, λ ).

Suppose then that each player asks himself or herself: " Knowing the strategies of the other players, and treating the strategies of the other players as set in stone, can I benefit by changing my strategy?

Suppose a lossless antenna has a radiation pattern given by:

Suppose is a mapping of surfaces parameterized by and.

* Suppose that is a sequence of Lipschitz continuous mappings between two metric spaces, and that all have Lipschitz constant bounded by some K. If ƒ < sub > n </ sub > converges to a mapping ƒ uniformly, then ƒ is also Lipschitz, with Lipschitz constant bounded by the same K. In particular, this implies that the set of real-valued functions on a compact metric space with a particular bound for the Lipschitz constant is a closed and convex subset of the Banach space of continuous functions.

Suppose f were injective, which means the pieces of S cut out by the squares stack up in a non-overlapping way.

* Suppose we have a language L recognized by both the RP algorithm A and the ( possibly completely different ) co-RP algorithm B.

Suppose V and W are vector spaces over the field K. The cartesian product V × W can be given the structure of a vector space over K by defining the operations componentwise:

Suppose that C is a twice continuously differentiable immersed plane curve, which here means that there exists parametric representation of C by a pair of functions such that the first and second derivatives of x and y both exist and are continuous, and

Suppose z is defined as a function of w by an equation of the form

Suppose Then, by the equivalence of the permutation representation and the group action.

Suppose bidding for an item placed by Anne starts at $ 1. 00 and that the bid increment amount in this price range is $. 25.

Suppose M is some 2-dimensional Riemannian manifold ( not necessarily compact ), and we specify a " triangle " on M formed by three geodesics.

Suppose that a worm crawls along a 1 metre rubber band and, after each minute, the rubber band is uniformly stretched by an additional 1 metre.