What is the word problem group theory?
In mathematics, especially in the area of abstract algebra known as combinatorial group theory, the word problem for a finitely generated group G is the algorithmic problem of deciding whether two words in the generators represent the same element.
When comparing groups or taking away from a group in a word problem we?
When you compare two groups, you either add or subtract. ? Tip: The words more and fewer are used in this type of problem. In these problems, DO NOT think that “more” is only for adding and “fewer” is only for subtracting. Both words can be used for either addition and subtraction.
What is a word problem in math called?
This article is about a type of exercise in mathematics education. For other uses, see Word problem (disambiguation). As most word problems involve a narrative of some sort, they are sometimes referred to as story problems and may vary in the amount of technical language used.
Who came up with word problems?
The word problem is one of three algorithmic problems for groups proposed by Max Dehn in 1911. It was shown by Pyotr Novikov in 1955 that there exists a finitely presented group G such that the word problem for G is undecidable.
What are the different types of word problems?
You can use three common types of word problems — part-part whole, separate and join and multiply and divide — for everything from counting pennies to calculating a tip.
What is a Comparing word problem?
COMPARISON problems are the type of problems looked at this week, which involve figuring our similarities or differences between sets. Difference Unknown: One type of compare problem involves finding out how many more are in one set than another.
What happens when you compare equal groups?
The word problem is an equal-groups problem, because the problem mentions that each friend gets an equal amount. If the problem said that each friend gets the same number of candies, it would still be an equal-groups problem because same and equal mean the same thing.
What are examples of word problems?
Mathematical Word Problems
- Rachel has 17 apples.
- Jack has 8 cats and 2 dogs.
- if there are 40 cookies all together and A takes 10 and B takes 5 how many are left.
- If Jane has 23 cats and I have 2 cats, and then Jane gives me 5 cats, how many more cats does Jane have than I?
- Rhonda has 12 marbles more than Douglas.
What is word problem in science?
A word problem is a mathematical exercise which is in the form of a hypothetical question that needs mathematical analysis and equations to be solved.
What are word problems?
A word problem is a few sentences describing a ‘real-life’ scenario where a problem needs to be solved by way of a mathematical calculation.
Why do students struggle with word problems?
One of the biggest reasons why some students struggle with word problems is because they aren’t just regular math problems – they involve reading! And more than that, students have to be able to fully comprehend what is happening in the problem in order to figure out how to solve it.
How many algorithmic problems are unsolvable?
Two algorithmic problems are related to each such class: the word problem for groups from Kα , and the problem of recognizing whether or not an arbitrary group belongs to Kα . It was found that for any non-empty class Kα at least one of these algorithmic problems is unsolvable. The same applies to semi-groups as well.
Is the word problem in combinatorial group theory solvable?
As a result of its unsolvability, several other problems in combinatorial group theory have been shown to be unsolvable as well. It is important to realize that the word problem is in fact solvable for many groups G.
Is there a universal solvable word problem group?
Corollary: There is no universal solvable word problem group. That is, if G is a finitely presented group that contains an isomorphic copy of every finitely presented group with solvable word problem, then G itself must have unsolvable word problem.
Is there a maximum degree of unsolvability of a problem?
Many studies of algorithmic problems arising in mathematics showed that each such problem had, in the general case, a maximum degree of unsolvability, while their special instances (e.g. the word identity problem in specific semi-groups or groups) may have any pre-given degree of unsolvability.