## Definitions Sentence Examples

- It was simply a case of differing
**definitions**of quid pro quo. - But admitting the validity of this criticism, and even going so far as to question the possibility of ever devising absolutely inclusive and, at the same time, exclusive
**definitions**, no sufficient reason is adduced for giving up all attempt at morphological analysis. - With these
**definitions**it is now possible to prove the following six premisses applying to finite cardinal numbers, from which Peano 2 has shown that all arithmetic can be deduced i. - The
**definitions**of the finite ordinals can be expressed without use of the corresponding cardinals, so there is no essential priority of cardinals to ordinals. - Contrasting the above
**definitions**of number, cardinal and ordinals, with the alternative theory that number is an ultimate idea incapable of definition, we notice that our procedure exacts a greater attention, combined with a smaller credulity; for every idea, assumed as ultimate, demands a separate act of faith. - The arithmetic of rational numbers is now established by means of appropriate
**definitions**, which indicate the entities meant by the operations of addition and multiplication. - These entities are not created by mathematicians, they are employed by them, and their
**definitions**should point out the construction of the new entities in terms of those already on hand. - The arithmetic of real numbers follows from appropriate
**definitions**of the operations of addition and multiplication. - We frequently meet with cogredient and contragedient quantities, and we have in general the following
**definitions**:-(i) " If two equally numerous sets of quantities x, y, z,... - He is not prepared to exclude the great medieval pronouncements, or the modern Roman Catholic
**definitions**, from the list of dogmas; but on the whole he prefers to keep in view " one historical species " - Loofs suggests that he ought perhaps rather to say one individual type - that greatest group of Christian dogmas which " was created by the Greek spirit upon the soil of the gospel " (Hist. - A discussion of these concepts and the various
**definitions**of angles in Euclidean geometry is to be found in W. - Let's address that by looking at two phenomena: the changing
**definitions**of poverty over time, and the effect of a large gap between the incomes of the rich and poor. - I am going to use
**definitions**of my own in order to draw a contrast between two ideas that I consider very differentâ€”one peaceful and one not. - What many children think of with dread, as a painful plodding through grammar, hard sums and harder
**definitions**, is to-day one of my most precious memories. - In investigating any subject there must occur at the beginning words and phrases which cannot be adequately understood until the pupil has made considerable advancement; yet I have thought it best to go on giving my pupil simple
**definitions**, thinking that, although these may be somewhat vague and provisional, they will come to one another's assistance, and that what is obscure to-day will be plain to-morrow. - He would transfer a question to metaphysical heights, pass on to
**definitions**of space, time, and thought, and, having deduced the refutation he needed, would again descend to the level of the original discussion.