# Pt1420 Unit 6 Assignment 1

Satisfactory Essays
493 Words
Grammar
Plagiarism
Writing
Score
Pt1420 Unit 6 Assignment 1
The free group with two generators a and b is composed of all finite strings that are formed from the four symbols a, a−1, b and b−1 given that no a is directly next to an a−1 and no b is directly next to a b−1. Two such strings can be concatenated and converted into a string of this type by repeatedly replacing the "forbidden" substrings with the empty string. For example: abab−1a−1 concatenated with abab−1a yields abab−1a−1abab−1a, which contains the substring a−1a underlined in the example, and so the “forbidden” string gets cancelled and reduced to abab−1bab−1a, which again contains the substring b−1b underlined in the example, which then gets reduced to abaab−1a. It can be checked that the group formed from the set of those strings with …show more content…
For instance, one of the strings in the set aS(a^(-1) ) may be 〗aa^(-1) b which, because of the “forbidden” rule that I discussed earlier which states that a must not appear next to a^(-1), aa^(-1)gets cancelled and reduced to the string b. Similarly, the set contains all the strings that start with 〗a^(-1) (for example the string 〗〖aa〗^(-1) a^(-1) which reduces to〗〖 a〗^(-1)). In this way, the set aS(a^(-1) ) contains all the strings that start with b, b^(-1) and〖 a〗^(-1).
This decomposed the group F2 into four pieces (in addition to the singleton {e} –singleton means a single element in a set-), then by multiplying with a or b two of them were "shifted", then "reassembled" two pieces to make one copy of F_2 and the other two to make another copy of F_2. That is exactly what Banach and Tarski wanted to do to that sphere.
Step 2
In order to find a free group of rotations of 3D space, i.e. that behaves just like (or "is isomorphic to") the free group F2, two orthogonal axes are taken, in this example I will take the x and z axes, and let A be a rotation of θ=arcoss(1/3) about the x axis (arcoss is defined as the one angle between 0 and π radians whose cos in this case is 1/3.), and B be a rotation

## You May Also Find These Documents Helpful

• Satisfactory Essays

Sequence A: AGA AGG GAG GAU UUG CAA GGU GGC CAA GAA UUA GGC GGC GGU CCC GGG GCG GGG AGU CUU CAA CCA…

• 366 Words
• 2 Pages
Satisfactory Essays
• Powerful Essays

From my table of values above, it is clear that the change of sign from negative…

• 2430 Words
• 10 Pages
Powerful Essays
• Powerful Essays

As a developer I was involved in collecting the requirements from business end user, according understood the business needs and involved in designing the universe for sales department ,As a first step we understand the structure of the universe and depending upon the fact tables n dimension tables created classes ,objects ,defined joins ,cardinalities ,created derived tables, custom Hierarchies .…

• 3509 Words
• 15 Pages
Powerful Essays
• Satisfactory Essays

Global variables are variables that are visible to every module in the program and its scope is the entire program so that all of the modules within the program can access a global variable. They can be declared in modules by simply setting up an assignment box and adding in the variables to the modules. In Pseudocode, you will simply write out the particular variable you want to declare and its value. Many programmers go against the idea of using global variables in modules but there are a few good sides to using global variables. For one, the global variables are very easy to find within modules and can be accessed throughout all of them. Global variables also make it easier to update…

• 439 Words
• 2 Pages
Satisfactory Essays
• Satisfactory Essays

These administrations help in building common dialect UIs. Discourse to Text gives a transcript of common dialect into content. Artificial intelligence is utilized to join linguistic and dialect structures with the preparing of voice motion for a more exact recognizable proof of words. Then again, Text to Speech benefit incorporates discourse from a content document while altering cadence and sound. The words are integrated progressively in a few dialects.…

• 303 Words
• 2 Pages
Satisfactory Essays
• Better Essays

Wallace Design Group owned by Kevin Wallace is an architectural services company. The location is in Farmers Branch, Texas. Kent Wallace, the marketing director, resides in California and remotely operates in the office. The organization is very small, yet group communication is very poor.…

• 1193 Words
• 4 Pages
Better Essays
• Good Essays

1. What I found to be interesting in this week’s reading is something I never really thought about much and that’s the thought of waste. Mainly the thought of toileting issues was there a set area for going to the bathroom? Another thing that struck up a conversation with my boyfriend was the Inca tribe not having a form of conventional writing the whole knots and colors is very fascinating to me.…

• 361 Words
• 2 Pages
Good Essays
• Better Essays

Deﬁnition 2.2. Let S be a set and let FS be the free group on S. Let R be a set of words…

• 4198 Words
• 17 Pages
Better Essays
• Satisfactory Essays

3. Construct a regular grammar over the alphabet Σ = {a, b, c, d} whose…

• 367 Words
• 5 Pages
Satisfactory Essays
• Good Essays

Actual sequence of characters that matches pattern and is classified by a token Identifiers: x, count, name, etc……

• 2518 Words
• 11 Pages
Good Essays
• Satisfactory Essays

L  a  b  a * L  a  b   L a *…

• 840 Words
• 15 Pages
Satisfactory Essays
• Powerful Essays

strings under the subtree of u. We analyze the pruning functionality of such signatures based on the set resemblance between the…

• 15261 Words
• 62 Pages
Powerful Essays
• Better Essays

Abstract machines that operate as transducers are of interest in connection with the translation of languages. The following transducer produces a sentence…

• 1359 Words
• 6 Pages
Better Essays
• Satisfactory Essays

{ w | w has length ≥ 3 and its 3rd symbol is 0 }…

• 1027 Words
• 5 Pages
Satisfactory Essays
• Good Essays

The set of all nonempty strings over an alphabet is denoted by . That is,…

• 8841 Words
• 36 Pages
Good Essays