On this page you'll find 10+ example sentences with Adic. Discover the meaning, how to use the word correctly in a sentence.
Adic meaning
- Relating to adicity
- Carrying the I-adic topology for some ideal I of the ring.
Using Adic
- The main meaning on this page is: Relating to adicity | Carrying the I-adic topology for some ideal I of the ring.
Context around Adic
- Average sentence length in these examples: 22.7 words
- Position in the sentence: 7 start, 10 middle, 3 end
- Sentence types: 20 statements, 0 questions, 0 exclamations
Corpus analysis for Adic
- In this selection, "adic" usually appears in the middle of the sentence. The average example has 22.7 words, and this corpus slice is mostly made up of statements.
- Around the word, centre, numbers, expansions and decadic stand out and add context to how "adic" is used.
- Recognizable usage signals include above 10 adic numbers have and as 10 adic numbers with. That gives this page its own corpus information beyond isolated example sentences.
- By corpus frequency, "adic" sits close to words such as abattoirs, abike and ablative, which helps place it inside the broader word index.
Example types with adic
The same corpus examples are grouped by length and sentence type, making it easier to see the contexts in which the word appears:
As noted above, 10-adic numbers have a major drawback. (10 words)
Naturally, this 2-adic integer has no corresponding natural number. (10 words)
Notation There are several different conventions for writing p -adic expansions. (11 words)
Extensions of the concept p-adic numbers main The p-adic numbers may have infinitely long expansions to the left of the decimal point, in the same way that real numbers may have infinitely long expansions to the right. (39 words)
The p in " p -adic" is a variable and may be replaced with a prime (yielding, for instance, "the 2-adic numbers") or another placeholder variable (for expressions such as "the ℓ-adic numbers"). (34 words)
From this definition, it is clear that positive integers and positive rational numbers with terminating decimal expansions will have terminating 10-adic expansions that are identical to their decimal expansions. (30 words)
Example sentences (20)
The p in " p -adic" is a variable and may be replaced with a prime (yielding, for instance, "the 2-adic numbers") or another placeholder variable (for expressions such as "the ℓ-adic numbers").
Extensions of the concept p-adic numbers main The p-adic numbers may have infinitely long expansions to the left of the decimal point, in the same way that real numbers may have infinitely long expansions to the right.
Introduction This section is an informal introduction to p-adic numbers, using examples from the ring of 10-adic (decadic) numbers.
We can create 10-adic expansions for negative numbers as follows : : : and fractions which have non-terminating decimal expansions also have non-terminating 10-adic expansions.
The Alcohol and Drug Information Centre (ADIC) has issued a statement regarding the proposal by the Commissioner General of Excise to introduce alcohol at a lower price.
Although for p-adic numbers p should be a prime, base 10 was chosen to highlight the analogy with decimals.
As noted above, 10-adic numbers have a major drawback.
For a prime p, the p-adic numbers arise by completing the rational numbers with respect to a different metric.
From this definition, it is clear that positive integers and positive rational numbers with terminating decimal expansions will have terminating 10-adic expansions that are identical to their decimal expansions.
Hence we want to define a notion of infinite sum which makes these expressions meaningful, and this is most easily accomplished by the introduction of the p -adic metric.
In the theory of Shimura varieties it associates automorphic representations of other groups to certain l -adic Galois representations as well.
Iterating with odd denominators or 2-adic integers The standard Collatz map can be extended to (positive or negative) rational numbers which have odd denominators when written in lowest terms.
It is also possible to write p -adic expansions so that the powers of p increase from left to right, and digits are carried to the right.
Naturally, this 2-adic integer has no corresponding natural number.
Notation There are several different conventions for writing p -adic expansions.
Note that this is not the only way to write p -adic numbers – for alternatives see the Notation section below.
So far this article has used a notation for p -adic expansions in which powers of p increase from right to left.
Ternary relations may also be referred to as 3-adic, 3-ary, 3-dimensional, or 3-place.
The I-adic topology is Hausdorff if and only if the intersection of all powers of I is the zero ideal (0).
The other rational numbers can be expressed as 10-adic numbers with some digits after the decimal point.