1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
rusak2 [61]
3 years ago
12

What's 1 + 1? Get it correct for free points.

Mathematics
2 answers:
Taya2010 [7]3 years ago
6 0
................2...............
frez [133]3 years ago
6 0

Answer:

answer

Step-by-step explanation:

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  x  =.9999999999999999999...  

10x=9.99999999999999999...  

10x=9+.99999999999999...  

10x=9+x  

Simplify by subtracting x from both sides.

9x=9  

x=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,S(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,S(0),S(S(0)),S(S(S(0))),S(S(S(S(0)))),S(S(S(S(S(0)))),…  

Further explained:

We know that we had nothing, and added something to it, and got something:

Nothing + Something = Successor of nothing.

0+__=S(0)  

We also know that there is nothing closer to 0, than the thing that comes after 0.

0+S(0)=S(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+S(0)=S(0)  

0+1=S(0)  

0+1=1  

0,1,S(S(0)),S(S(S(0))),S(S(S(S(0)))),S(S(S(S(S(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+S(0)=1;1+S(0)=S(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

S(1)=2  

The successor of 1 IS 2.

Thus:

0+S(0)=1;1+S(0)=S(1)=2  

Simplify:

0+1=1;1+1=S(1);S(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.

You might be interested in
A ball is thrown straight out at 80 feet per second from an upstairs window that's 15 feet off the ground. Find the ball's horiz
Alex73 [517]

Answer:

Step-by-step explanation:

In order to find the horizontal distance the ball travels, we need to know first how long it took to hit the ground. We will find that time in the y-dimension, and then use that time in the x-dimension, which is the dimension in question when we talk about horizontal distance. Here's what we know in the y-dimension:

a = -32 ft/s/s

v₀ = 0 (since the ball is being thrown straight out the window, the angle is 0 degrees, which translates to no upwards velocity at all)

Δx = -15 feet (negative because the ball lands 15 feet below the point from which it drops)

t = ?? sec.

The equation we will use is the one for displacement:

Δx = v_0t+\frac{1}{2}at^2 and filling in:

-15=(0)t+\frac{1}{2}(-32)t^2 which simplifies down to

-15=-16t^2 so

t=\sqrt{\frac{-15}{-16} } so

t = .968 sec (That is not the correct number of sig fig's but if I use the correct number, the answer doesn't come out to be one of the choices given. So I deviate from the rules a bit here out of necessity.)

Now we use that time in the x-dimension. Here's what we know in that dimension specifically:

a = 0 (acceleration in this dimension is always 0)

v₀ = 80 ft/sec

t = .968 sec

Δx = ?? feet

We use the equation for displacement again, and filling in what we know in this dimension:

Δx = (80)(.968) +(0)(.968)^2 and of course the portion of that after the plus sign goes to 0, leaving us with simply:

Δx = (80)(.968)

Δx = 77.46 feet

5 0
3 years ago
ASAP!!! PLEASE help me with this question!
Aloiza [94]
Pretty sure it’s a circle , why would it be a rectangle and a right angle
6 0
3 years ago
Two wrongs and One right: vertical angles. Please help only 2-3 questions
luda_lava [24]

Answer:

Solution one is correct and solution 2 and 3 are incorrect

Step-by-step explanation:

You simply make an equation because for vertical angles 2 angles that are across from each other have the same value (in this case 2x+30 and 5x-36.)

The equation: 2x+30=5x-36---->3x=66----> x=22

Solution 1 is correct.

Hope this helped!

3 0
3 years ago
Read 2 more answers
Jane is building eight 3-legged stools. Each leg is 1/2 yard long. She can cut the legs from wooden rods that are sold in 2-yard
jonny [76]

Answer:

n = 6\,rods

Step-by-step explanation:

The total of legs needed to build the stools are:

x = (8) \cdot (3)

x = 24

Likewise the total length of the legs is:

L_{tot} = 24\cdot (0.5\,yd)

L_{tot} = 12\,yd

Lastly, the quantity of rods that needed to buy is:

n = \frac{12\,yd}{2\,\frac{yd}{rod} }

n = 6\,rods

6 0
3 years ago
What is -17 mod 8 I’m confused at the moment
alukav5142 [94]

Answer:

-136

Step-by-step explanation:

Given :

-17(|8|)

Mod of positive number is positive

So, |8|=8

-17(8)

=-136

Therefore,-17 mod 8 is -136

4 0
3 years ago
Other questions:
  • Depreciation is the decrease or loss in value of an item due to age, wear, or market conditions. We usually consider
    10·1 answer
  • Lamar and Jessie are multiplying 7/9 * 4/9
    14·1 answer
  • How do I multiply 30 and 4 1/3
    5·1 answer
  • If 36-k=4+k what is the value of K?
    14·2 answers
  • Tasha says that the expression 6.8w-4.7 can be simplified as 2.1w. Her teacher explains that this is not correct. What mistake d
    15·1 answer
  • R-32=2 please Help me on this
    12·1 answer
  • A total of 12,650 voters completed an online survey that asked if they are going to vote for a certain political canidate in an
    5·1 answer
  • PLEASE I HAVE 10 min TO FINISH THIS I NEED HELP
    7·2 answers
  • 11.
    14·1 answer
  • Add 2x4 - 6x3 + 5x to the difference between 9x3 + 8x2 - 2 and 4x4 - 2x2 + 8x - 5.
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!