What is 2 + 2? Its kinda important. for a very important school project.

I do not know how to solve this incredibly difficult question. The complexity rivals those of the millennial problems. Instead, I’ll let reddit user u/sellopou speak his words.

Take a computational approach to the problem. Specifically, consider the encoding of natural numbers in the simply-typed lambda calculus called Church numerals. In this encoding, the number 2 is represented by a function that looks like this:

2 ≡ λf.λx.f (f x)  

In other words, the number two is a function that takes a function and some value (let's assume that we're comfortable with currying here), and applies the function twice to the value. In general, a number n is represented by a function that takes a function and some value and applies f to the value n times.

Using the Church encoding, you can define operations on the numbers as well. In this case, you're interested in plus, which takes two numbers and returns a number

plus ≡ λm.λn.λf.λx.???  

So what's in the body? Well, the body has to be n + m applications of f to the value x. If we pass f and x to n, we get n applications–call that r, and if we apply m to f and r, that'll be m + n applications of f:

plus ≡ λm.λn.λf.λx.m f (n f x)  

So the expression 2 + 2 using this encoding is:

plus 2 2 ≡ (λm.λn.λf.λx.m f (n f x)) (λf.λx.f (f x)) (λf.λx.f (f x))  

Now β-reduce until you get the result:

plus 2 2 ≡ (λm.λn.λf.λx.m f (n f x)) (λf.λx.f (f x)) (λf.λx.f (f x))  

        ↦ (λn.λf.λx.(λf.λx.f (f x)) f (n f x)) (λf.λx.f (f x))  

        ↦ (λf.λx.(λf.λx.f (f x)) f ((λf.λx.f (f x)) f x))  

        ↦ (λf.λx.(λx.f (f x)) ((λf.λx.f (f x)) f x))  

        ↦ (λf.λx.(λx.f (f x)) ((λx.f (f x)) x))  

        ↦ (λf.λx.(λx.f (f x)) (f (f x)))  

        ↦ (λf.λx.f (f (f (f x  

        ≡ 4.  

But now, let's bust out of this theoretical prison and say we have a number 0 in some representation that we can actually work with, as well as a function add1 that knows how to increment a number in that representation. Well, then we can get a useable representation out of our church numeral, by applying to the numeral to add1 and the value:

4 add1 0 = 4  

the required function is .

step-by-step explanation:

from the given table it is noticed that the graph passing through (-3,7), (0,4), (3,1) and (8,-4).

it is a linear function because the value of y is decrease by one as the value of x increase by 1.

the slope of the function is

the slope of the function is -1 and the y-intercept is 4.

the slope intercept form is

where, m is slope and b is y-intercept.

therefore the required function is . the graph of this function is shown below.

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.