Answers
Answer:
A more complex question has rarely been asked.
Principia Mathematica took nearly a thousand pages to prove that 1+1=2. It does meander a bit, but had they wanted to prove 1+1=2 alone, it could have done so in 500 pages.
Mathematically speaking, the definition of 1 is:
There exists a number such that when multiplied upon an element of a specified set, yields the element of the specified set.
It is also defined as:
1.0000000000000000000000…
.9999999999999999999999999…
as the set of all singletons.
a singleton is a set with exactly 1 element.
These 4 definitions work in tandem with one another.
For example:
1=1
Divide both sides by 3.
1/3=1/3
Rewrite.
1/3=.33333333333333333...
Multiply both sides by 3.
1=.9999999999999999999...
Similarly:
If =.9999999999999999999...
10=9.99999999999999999...
10=9+.99999999999999...
10=9+
Simplify by subtracting x from both sides.
9=9
=1
.99999999999999999999...=1
As the set of all singletons, 1 is also THE element that represents the set of all single entities.
That is to say: if you have 7 erasers. What you really have is a set of 7 single entities. The definition of 7 becomes: 1 + 1 + 1 + 1 + 1 + 1 + 1; and not as is commonly believed as: 6 + 1.
There is an argument for 7 to be defined as 6 + 1, but this argument is a corollary of the Peano Axioms which in turn argues that there exists a set with absolutely nothing in it {} and a set with exactly something in it {x}. More on this later.
The Principia Mathematica uses Peano's (from the Peano Axioms mentioned earlier) work and notation to expertly slice through the many nuances pertaining to this question.
This is something we will not do; but hopefully, we will also be able to effectively demonstrate why 1 + 1 = 2 in less than 1000 pages.
We will assume these basic principles of number theory:
There exists a number such that when multiplied to an element of a specific set, yields that element of the specific set.
There exists a number such that when added to an element of a specific set, yields that element of the specific set.
If we again assume to have only two sets, a set that is empty: {} containing no elements, and a set that is not empty {x} containing an element. We realize that Consequently, we went from nothing {}, to something {x}. This means that {x} is the successor to {}, as the next step up from nothing, is something.
As such we now have two elements:
Nothing, {}, and something that comes after {}, this something is called the successor, and it is the Successor of nothing.
in written notation we have:
{} and { the Successor of nothing }
Rewritten:
{0, the thing that comes after 0}
Further reworded:
{0, Successor (0) }
Reduced further:
0,(0)
Where S(0) stands in place of ‘the successor’. Further, we know there are an infinite number of possible Natural numbers, and we get:
{0, Successor of 0, the successor of the successor of 0, the successor of the successor of the successor of 0,…}
Further reduced:
0,(0),((0)),(((0))),((((0)))),(((((0)))),…
Further explained:
We know that we had nothing, and added something to it, and got something:
Nothing + Something = Successor of nothing.
0+__=(0)
We also know that there is nothing closer to 0, than the thing that comes after 0.
0+(0)=(0)
This implies that S(0) is the smallest increment possible from natural number to next natural number.
As a consequence, we now have two discovered entities: Something, and Nothing.
Let’s give them names.
We have decided that
Nothing = 0 .
0 = Nothing.
S(0) is the something that comes after nothing.
We define a new symbol: 1, to be: 1 = S(0)
This is to say that 1 IS the symbol that succeeds 0;
We could have drawn any shape to define the number that succeeds 0; we chose to draw a 1.
0+(0)=(0)
0+1=(0)
0+1=1
0,1,((0)),(((0))),((((0)))),(((((0)))),…
We now have definitions for 0, and 1. What about a definition for the thing that comes after one? The successor of 1?
As we know S(0) is the smallest increment available, and we are interested in finding S(0)’s successor we investigate:
The successor to the successor of Nothing:
0+(0)=1;1+(0)=(1)
This reads:
The successor of the successor of nothing IS the successor of one
And now… we need a new symbol.
We define the
(1)=2
The successor of 1 IS 2.
Thus:
0+(0)=1;1+(0)=(1)=2
Simplify:
0+1=1;1+1=(1);(1)=2.
Further:
0+1=1;1+1=2;2=2.
1 has many different properties; but all of the properties and their resulting definitions have little to do with why 1 + 1 = 2. And that 1 + 1 = 2 is a byproduct of properties inherent to Natural numbers.
Step-by-step explanation:
Related Questions
what is the factor of x^2 + 2x - 3
Answers
Answer:
(x + 3)(x - 1)
Step-by-step explanation:
Given
x² + 2x - 3
Consider the factors of the constant term (- 3) which sum to give the coefficient of the x- term (+ 2)
The factors are + 3 and - 1 , since
3 × - 1 = - 3 and 3 - 1 = + 2 , then
x² + 2x - 3 = (x + 3)(x - 1) ← in factored form
What is the factor of x² + 2x - 3
Solution:-x² + 2x - 3[tex] \rightarrow [/tex] x² + 3x - x - 3 = 0
[tex] \rightarrow [/tex] x(x + 3) -1(x + 3) = 0
[tex] \rightarrow [/tex] (x + 3) (x - 1) = 0
[tex] \therefore [/tex] Either, x + 3 = 0 => x = -3 and x - 1 = 0 => x = 1
So, x = -3 and 1
The factor of x² + 2x - 3 is -3 and 1. [Answer]Triangle A'B'C' is the image of ABC under a rotation about point P.
Determine the angle of rotation.
-75
-45
45
75
Answers
Answer:
its 45
Step-by-step explanation
It's right I did it on khan
For the first week of January, Kim Walker worked 45.25 hours. Kim earns 10.90 an hour. Her employer pays overtime for all hours worked in excess of 40 hours per week and pays 1.5 times the hourly rate for overtime hours.
Answers
Answer:
Gross pay when she works 46 hours a week = 532 dollars per week
Step-by-step explanation:
Complete question
Find gross pay when she works 46 hours a week
Solution
For working hours less than or equal to 40 hours, kim earns 10.90 per hour
For working hours higher than the basic 40 hours of working, the per hour rate increases by 1.5 time = 1.5 *10.90 = 16 dollars per hour
Gross pay for 46 working hours = 40 *10.90 + 6*16 = 532 dollars per week
ACELLUS PLZ HELP ASAP
6101
4629
10730
What is the probability that a given student is a
graduate, given that he or she is on financial aid?
Answers
Answer:
The probability that a given student is a graduate, given that he or she is on financial aid, is 30.8%.
Step-by-step explanation:
To determine what is the probability that a given student is a graduate, given that he or she is on financial aid, the following calculation must be performed:
6101 = 100
1879 = X
1879 x 100/6101 = X
187,900 / 6101 = X
30,798 = X
Therefore, the probability that a given student is a graduate, given that he or she is on financial aid, is 30.8%.
Answer:
31%Step-by-step explanation:
in which sentence is the literary device litotes used?
Answers
The correct sentence is "He commented that her house was no palace".
What is litotes?“Litotes is a figure of speech and a form of understatement in which a sentiment is expressed ironically by negating its contrary.”
A litote is an statement that expresses the affirmative by saying the negative of the contrary.
The other statements are all statements, they do not give any indication of a deeper level of meaning.
Another example of a litote is: That wasn't the messiest house I've ever seen. In this statement, the house is being described as messy by saying that it is not.
The correct sentence is "He commented that her house was no palace".
Learn more about Litotes ;
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What is the area of this face?
Answers
Answer:
Hello! answer: 180
Step-by-step explanation:
what I did to find answer is cut them into pieces I cut the m into 3 pieces and now just have to multiply my base x height so for the left one I did 12 x 6 = 72 for the middle I did 6 x 6 = 36 and for the right one I did 12 x 6 = 72 I add these up so...
72 + 36 + 72 = 180 so the surface area is 180! I hope this helps!
V = 127th
1. 12(3.14) (1) = 37.68
2
3
4
5
6
7
8
9
10
Answers
Answer:
988
Step-by-step explanation:
what's your answer??>????????????????????????
Answers
Answer and Step-by-step explanation:
The answer is parallelograms.
This is because they all have 4 sides and have 2 pairs of parallel sides, which is enough to say that it is a parallelogram.
#teamtrees #PAW (Plant And Water)
Answer:
parallelogramsStep-by-step explanation:
As,
In the picture there is a parallelogram, rhombus, rectangle and a square.
We know,
Properties of parallelogram:-
Opposite sides are equal and parallel Diagonals bisect each other.Sum of any two adjacent angles is 180°All the above conditions are also same In a rhombus, rectangle and a square.
Hence,
Parallelogram best describes all the above shapes
James is getting ready for wrestling season. As part of his preparation, he plans to lose 5% of his body weight James currently weighs 100 pounds How much will he weigh, in pounds, after he loses 5% of his weight
Answers
Multiply 100 pounds by 5%: 100 x 0.05 = 5 pounds.
Subtract that from the original weight:
100 - 5 = 95
He will weigh 95 pounds
There are 10 2/15 kg of watermelons and coconuts on a truck. The weight of the watermelons is 3 3/5 times that of the coconuts. How heavy are the coconuts on the truck, in kg?
Answers
Answer:
2 7/76 kg
Step-by-step explanation:
Let the weight of
Watermelons = x
Coconut = y
There are 10 2/15 kg of watermelons and coconuts on a truck.
x + y = 10 2/15
x = 10 2/15 - y
x = 152/15 - y.... Equation 1
The weight of the watermelons is 3 3/5 times that of the coconuts.
x = 3 3/5 × y
x = 18/5 × y
x = 18y/5
How heavy are the coconuts on the truck, in kg?
Find y
We substitute 18y/5 for x in Equation 1
x = 152/15 - y
18y/5 = 152/15 - y
18y /5 + y = 152/15
Multiply through by 15
18y/5 × 15 + y × 15 = 152/15 × 15
3 × 18y + 15y = 152
54y + 15y = 152
69y = 152
y = 152/69
y = 2 14/152
y = 2 7/76 kg
Therefore, the weight of the coconuts are 2 7/76 kg
how to right a number in standerd form
Answers
Answer:
How to write numbers in standard form:
Write the first number 8.
Add a decimal point after it: 8.
Now count the number of digits after 8. There are 13 digits.
So, in standard form: 81 900 000 000 000 is 8.19 × 10¹³
Step-by-step explanation:
please mark this answer as brainliest
(Robert LaClerq is paid a regular wage of $9.50 an hour, overtime at the rate of 1 times the regular rate for all hours worked over 8 in any weekday, and overtime at the rate of 2 times the regular rate for hours worked on Saturdays, Sundays, and holidays. During the week ended February 14, LaClerq worked the following days and hours. Calculate the regular hours worked and the overtime hours worked. Then answer the questions that follow.)
Answers
Answer:
Day Total hours worked regular hours Overtime hours
Monday 7 7 0
Tuesday 10 8 2
Wednesday 8 8 0
Thursday 10 8 2
Friday 11 8 3
Saturday 2 2 0
Step-by-step explanation:
The remaining part of the question is attached
Solution
A person can work maximum of 8 hours in a day
Overtime paid during week day = 1.5 times of $ 9.50 = $14.25
Overtime paid during weekend = 2 times of $ 9.50 = $19
Day Total hours worked regular hours Overtime hours
Monday 7 7 0
Tuesday 10 8 2
Wednesday 8 8 0
Thursday 10 8 2
Friday 11 8 3
Saturday 2 2 0
1. The regular hours that Robert LaClerq worked is 41 hours (39 for weekdays and 2 for weekend), while the overtime hours is 7 hours.
2. The calculation of Robert's regular pay is $370.50 (39 x $9.50).
3. The calculation of Robert's overtime pay during weekdays = $66.50 (7 x $9.50).
4. The calculation of Robert's overtime pay on weekends = $38.00 (2 x $19.00).
What is Overtime Pay?Overtime pay is the wage payment to an earner for working above the normal (regular) working hours.
Data and Calculations:Wages per hour for regular hours = $9.50
Overtime pay during weekdays = $9.50 per hour
Overtime pay during weekends = $19 per hour ($9.50 x 2)
Day Total hours Regular Overtime
worked hours hours
Monday 7 7 0 (7 - 7)
Tuesday 10 8 2 (10 - 8)
Wednesday 8 8 0 (8 - 8)
Thursday 10 8 2 (10 - 8)
Friday 11 8 3 (11 - 8)
Saturday 2 2 0 (2 - 2)
Total hours 48 41 7
Thus, Robert's total earnings for the week is $475 ($370.50 + $66.50 + $38.00).
Learn more about overtime pay at https://brainly.com/question/13353961
The graph of (1) Is shown. Which graph represents g(x) = S(2x)?
Answers
Please help
Which line is perpendicular to 4y+3x=12?
A)3x+4y=8
B)y=-3x+8
C)y+4x=-3
D)8x-6y=18
Answers
Answer:
D) 8x - 6y = 18
Step-by-step explanation:
The general equation of a line is;
y = mx + c
m is the slope and c is the y-intercept
so for;
4y + 3x = 12
4y = -3x + 12
divide through by 4
y = -3/4x + 3
the slope here is -3/4
To get the other line, we divide -1 by the slope of the first line
This is because when two lines are perpendicular, the product of their slopes is -1
So the slope of the line we are looking for is -1 divide by -3/4 = 4/3
Let us take a look at option D
8x - 6y = 18
6y = 8x - 18
divide through by 2
3y = 4x - 9
divide through by 3
y = 4/3(x) - 3
So as we can see, we have our slope as 4/3 and this option is our answer
A 35 foot ladder is set against the side of a house so that it reaches up 28 feet. If Bentley grabs the ladder at its base and pulls it 4 feet farther from the house, how far up the side of the house will the ladder reach now? (The answer is not 24 ft.) Round to the nearest tenth of a foot.
Answers
Answer:24.5
Step-by-step explanation:
a^2+ (25)^2 =35^2
a^2 +625=1225
a^2=600
a=24.494897
a=24.5
The math department is putting together an order for new calculators. The
students are asked what model and color they prefer,
Answers
Answer:
D
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
A P # X
please help i have been struggling
Answers
Answer:
6000
Step-by-step explanation:
Find the lateral area and surface area of a cone with a radius of 12 and a height of 21
Answers
Answer:
The Lateral Surface Area is 911.32 square unit and
Total Surface Area is 1361.7 square unit.
Step-by-step explanation:
For a given Cone
Radius (r) = 12
Height (h) = 21
For Lateral Surface Area
Formula:A = πr√r² + h²
A = 3.14 × 12 × √(12)² + (21)²
A = 3.14 × 12 × √144 + 441
A = 3.14 × 12 × √585
A = 37.68 × 24.18
A = 911.32 square unit
Now,
For Total Surface Area
Formula:A = πrl + πr²
For Slant height (l)
l² = r² + h²
l² = (12)² + (21)²
l² = 144 + 441
l² = 585
l = 24.18
So,
A = πrl + πr²
A = πr(l + r)
A = 3.14 × 12 × (24.14 + 12)
A = 3.14 × 12 × 36.14
A = 1361.7 square unit
Thus, The Lateral Surface Area is 911.32 square unit and Total Surface Area is 1361.7 square unit.
-TheUnknownScientist
Step-by-step explanation:
Hope it's helpful to you dear frnd ☺️
How do I find the base and height? I know how to find the area, but I don't think I can find that without the base and height...
Answers
Answer:
Hello! answer: base = 47
Step-by-step explanation:
area = base × height ÷ 2 or base × height × 1/2
Find the surface area of the
regular hexagonal prism.
4 cm 12 cm
3.5 cm
Answers
Answer:
the surface of hexagonal prism is 12 cm
A material has an initial quantity of 20 units. Which equation models the amount of the material, y, growing exponentially at a rate of 17% for time, X?
y = 20(1.17)x
y=20(2.7)x
y=20(0.83)x
y=20(17)x
y = 17(1.2)x
Answers
y=20[tex]2.7^{x}[/tex] is the equation models that describes the growth rate of metal whose initial quantity is 20 units.
What is exponential functions?It is inverse of the logarithmic functions.
How to form exponential function?We have been given the initial quantity of metal which is 20 units
and it is growing exponentially at a rate of 17% for time x
So the required equation will be y=20 *e to the power x*17%
value of e is 2.718. so the equation becomes y=20(2.7)to power x
Learn more about exponential functions at https://brainly.com/question/2456547
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Find m and n...
Help plz
Answers
Answer:
m and 100are co-interior angles
so;
m+100=180. (being sum of co-interior angles)
m=180-100
m=80
like wise;
n=100
Find the area of the triangle below.
Be sure to include the correct unit in your answer.
m
4yd
14 yd
17 yd
Answers
To Find :
The area of triangle whose side are 4 yard, 14 yard and 17 yard.
Solution :
We will use Heron's formula to find area of the triangle.
So,
[tex]s = \dfrac{a+b+c}{2}\\\\s = \dfrac{4+14+17}{2}\\\\s = 17.5[/tex]
Now, heron's formula is :
[tex]A = \sqrt{s(s-a)(s-b)(s-c)}[/tex]
Putting all given values in above equation :
[tex]A = \sqrt{17.5\times (17.5-4)\times(17.5-14)\times(17.5-17)}\\\\A = \sqrt{17.5\times 13.5\times 3.5\times 0.5}\\\\A = 20.33\ yard^2[/tex]
Hence, this is the required solution.
Function g can be thought of as a translated (shifted) version of f(x)=x^2 Write the equation for g(x),
Answers
Answer:
g(x) = (x - a)² or
g(x) = (x + a)² or
g(x) = x² + a or
g(x) = (x + b)² + a or
g(x) = (x + b)² - a or
g(x) = (x - b)² + a or
g(x) = (x - b)² - a
Step-by-step explanation:
Given equation:
f(x) = x²
This is the equation of a parabola with turning points at (0,0) facing up.
Now;
g(x) which is a shifted version of f(x) will have one of many forms depending on the nature of translation.
If f(x) = x² is shifted to the right by a units, then;
g(x) = (x - a)²
If f(x) = x² is shifted to the left by a units, then;
g(x) = (x + a)²
If f(x) = x² is shifted upwards by a units, then;
g(x) = x² + a
If f(x) = x² is shifted downwards by a units, then;
g(x) = x² - a
If f(x) = x² is shifted upwards by a units and to the left by b units, then;
g(x) = (x + b)² + a
If f(x) = x² is shifted downwards by a units and to the left by b units, then;
g(x) = (x + b)² - a
If f(x) = x² is shifted upwards by a units and to the right by b units, then;
g(x) = (x - b)² + a
If f(x) = x² is shifted downwards by a units and to the right by b units, then;
g(x) = (x - b)² - a
A coordinate grid with 2 lines. The first line labeled f(x) passes through (negative 3, 3), (0, 2), and (3, 1). The second line labeled g(x) passes through the points at (negative 3, 0) and (0, 2)
What is the solution to the system of linear equations?
(–3, 0)
(–3, 3)
(0, 2)
(3, 1)
Answers
Answer:
(0, 2)
Step-by-step explanation:
the answer is (0, 2)
Plz help I’ll give u brainliest
Answers
Answer:
9
Step-by-step explanation:
All you have to do is subtract the temperatures once you get the final answer for them.
4 days, -7°C, = 43°C
5 days, -6°C, = 34°C
43 - 34 = 9
9°C = 9
~ LadyBrain
Need help will give thanks or brainliest
Answers
Step-by-step explanation:
success
................
Answer:
6 cm
Step-by-step explanation:
Well let me explain... It's saying that side AB has a length of 6 cm and side BC has a length of 10 cm. So we can already start labeling the sides with their given length and actually solve for AC.
Well we don't really got much to say about AC but what we do know is that side AB and AC are equivalent. Why? Cause when there's always a triangle that has two equal sides but one side bigger, the triangle is a isosceles.
So we can say that side AB is (Δ) from the top of the triangle all the way to the left corner (6 cm). Then side BC will be from the left corner to the right corner (10 cm) and side AC will be from the top to the right corner (6 cm).
If a1=10 and an+1=-5an-1 then find the value of a4
Please explain!
Answers
Answer:
[tex]a_4=-1271[/tex]
Step-by-step explanation:
We are given that:
[tex]a_1=10[/tex]
And:
[tex]a_{n+1}=-5a_n-1[/tex]
And we want to find:
[tex]a_4[/tex]
This is a recursive formula. So we can simply substitute in each value. For instance, a₂ will be:
[tex]a_2=a_{(1)+1}=-5a_{1}-1=-5(10)-1=-51[/tex]
Thus, a₃ will be:
[tex]a_3=a_{(2)+1}=-5a_2-1=-5(-51)-1=254[/tex]
Finally, a₄ will be:
[tex]a_4=a_{(3)+1}=-5a_3-1=-5(254)-1=-1271[/tex]
Answer please
76, 88, 81, 85, 86, 91, 68, 78, 72, 84, 82, 90, 69, 70, 75, 87, 79
Answers
Hi, I'm learning about graph theory. I just have a question: If a cycle is going in the same direction as another cycle, is it the same cycle? Example: Is ABCDA=BCDAB?
Answers
Answer:
no because it has a different starting and ending point
Step-by-step explanation:
hope it helps!