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sergeinik [125]
3 years ago
8

I need explanations for Mathematical Proofs.

Mathematics
1 answer:
erma4kov [3.2K]3 years ago
3 0

Answer:

Proofs employ logic expressed in mathematical symbols, along with natural language which usually admits some ambiguity. In most mathematical literature, proofs are written in terms of rigorous informal logic.

According to Bleiler-Baxter & Pair [22], for a mathematician, a proof serves to convince or justify that a certain statement is true. But it also helps to increase the understanding of the result and the related concepts. That is why a proof also has the role of explanation.

There are many different ways to go about proving something, we'll discuss 3 methods: direct proof, proof by contradiction, proof by induction. We'll talk about what each of these proofs are, when and how they're used. Before diving in, we'll need to explain some terminology.

Although I will focus on proofs in mathematical education per the topic of the question, first and foremost proofs are so hard because they involve taking a hypothesis and attempting to prove or disprove it by finding a counterexample. There are many such hypotheses that have (had) serious monetary rewards available.

In logic and mathematics, a formal proof or derivation is a finite sequence of sentences (called well-formed formulas in the case of a formal language), each of which is an axiom, an assumption, or follows from the preceding sentences in the sequence by a rule of inference.

All mathematicians in the study considered proofs valuable for students because they offer students new methods, important concepts and exercise in logical reasoning needed in problem solving. The study shows that some mathematicians consider proving and problem solving almost as the same kind of activities.

More information for you..

https://youtu.be/V5tUc-J124s

https://youtu.be/dMn5w4_ztSw

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18 girls I think.

Step-by-step explanation:

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3 years ago
Slader the internal revenue service claims it takes an average of 3.7 hours to complete a 1040 tax form, assuming th4e time to c
Vitek1552 [10]

Answer:

0.9953, 3.3629<x<4.0371

Step-by-step explanation:

Given that slader the internal revenue service claims it takes an average of 3.7 hours to complete a 1040 tax form, assuming th4e time to complete the form is normally distributed witha standard devait of the 30 minutes:

If X represents the time to complete then

X is N(3.7, 0.5) (we convert into uniform units in hours)

a) percent of people would you expect to complete the form in less than 5 hours

=100*P(x

b) P(b<x<c) = 0.50

we find that here

c = 4.0371 and

b = 3.3629

Interval would be

(3.3629, 4.0371)

6 0
3 years ago
The cost of 4 pounds of bananas is $1.88. What is the constant of proportionality that relates the cost in dollars, y, to the nu
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An important assumption underlying inferences from a linear regression is that variance in the response variable is reasonably c
rewona [7]

Answer:

A. True

Step-by-step explanation:

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1) Linear relationship : We need to check if the dependnet variable present a linear relationshipThe linearity assumption can best be tested with scatter plots in order to check if we have outliers in the data.

2) Multivariate normality : "The linear regression analysis requires all variables to be multivariate normal".  And we can check this with a histogram or a Q-Q-Plot, usually Normality can be checked with a goodness of fit test like the Kolmogorov-Smirnov test or Shapiro Wilks test.

3) No or little multicollinearity : "Multicollinearity occurs when the independent variables are too highly correlated with each other". And we can check this with a correlation matrix, variance inflation factor (VIF's), correlation index and other statistics.

4) No auto-correlation : The "Autocorrelation happens when the residuals are not independent from each other in the data". And usually we can test this with the Durbin-Watson test.

5) Homoscedasticity: MEans that we need constant variance for the linear model. The scatter plot is good way to check whether the data are homoscedastic. And we can interpret this condition as "that variance in the response variable is reasonably consistent across the range of an explanatory factor (otherwise known as homoscedasticity)"

So then the statement is TRUE.

5 0
3 years ago
40 percent of students survey said that they are night owls . If 300 students said that they are night owls how many students we
sattari [20]

Based on the calculations that 300 is 40%, 375 is considered 50% or halfway.. in this case, we must multiply 375 by 2 and we will discover how many students were surveyed:

375 x 2 = 750

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2 years ago
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