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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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A system of equations has no solution. If y = 8x + 7 is one of the equations, which could be the other equation?
julia-pushkina [17]
For the answer to the question above, a system of equations has no solution when the lines representing the equation are parallel but do not coincide. For two lines to be parallel, the must have the same gradient i.e. coefficient of x when y is made the subject of formula must be equal.
If one of the equations is
y = 8x + 7,
then the other equation will be
y = 8x - 7
5 0
3 years ago
Write the number 29085 in expanded form.​
Alex

Answer:

We expand a number to show the value of each digit.

29085:

20,000 + 9,000 + 000 + 80 + 5 = 29085

<em>Hope this helps!!</em>

6 0
3 years ago
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Is 0.09 squared a rational number?
Novay_Z [31]
Yes, 0.09 squared, or <span>0.0081, is a rational number.</span>
7 0
3 years ago
PLEASE HELP ASAP
Lesechka [4]

Answer:

A. f and h

Step-by-step explanation:

For a linear function the First Differences of the y-values must be a constant. i.e. if we take the difference between any two consecutive y values or values of f(x) it should be the constant. For this rule to work, x values must change by the same number every time, which is true for all three given functions.

For function f:

The values of f(x) are: 5,8,11,14

We can see the difference in consecutive two values is a constant i.e. 3, so the First Difference is the same. Hence, function f is a linear function.

For function g:

The values of g(x) are: 8,4,16,32

We can see the difference among two consecutive values is not a constant. Since the first differences are not the same, this function is not a linear.

For function h:

The values of h(x) are: 28, 64, 100, 136

We can see the difference among two consecutive values is a constant i.e. 36. Therefore, function h is a linear function.

5 0
3 years ago
"what is the binary equivalent of the decimal value 97?"
AleksandrR [38]
01100001 = 97 64+32+1=97  (if the leading bit is 0 it's usually not shown)
very easy
8 bits
Bit 1 Value 128
Bit 2 value 64
Bit 3 value 32
Bit 4 value 16
Bit 5 value 8
Bit 6 value 4
Bit 7 value 2
Bit  8 value 1
5 0
3 years ago
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