Position of moving body at time t

[Ostronomos]

Suppose you have a moving body at time t. Then it's position would be a function f that contains a domain representing time at t. Therefore, if one wishes to find the position, they would simply calculate the function f(t). Whereas at time t=3, the body is at f(3), and at t=2, the body is at f(2). Or at t=0, the initial position would be f(0).

Now, when the Greeks first wrestled with the concept of limits over two thousand years ago, they fell short of success. It was only in the last 200 years that we came develop the concept of limits to its fullest extent.

E.g. If a function contains an interval (a,b). Where c ∈ (a,b). Then the slope of the tangent at the curve would be f'(c). Where f'(c) is the position of the body at x=c. Or, x=t.

Is this correct?

 

[Ostronomos]

To whomever it may concern,

Correct me if I'm wrong, but is the derivative and slope of tangent just two alternative ways of interpreting the limit of first-principles definition?

This can be applied to the concept of motion in the real world. Specifically velocity.

Where x=c and (a,b) is an interval between which the function (assuming it's continuous) behaves? Note: c ∈ (a,b)

 

[River Sea]

Suppose you have a moving body at time t. Then it's position would be a function f that contains a domain representing time at t. Therefore, if one wishes to find the position, they would simply calculate the function f(t). Whereas at time t=3, the body is at f(3), and at t=2, the body is at f(2). Or at t=0, the initial position would be f(0).

Now, when the Greeks first wrestled with the concept of limits over two thousand years ago, they fell short of success. It was only in the last 200 years that we came develop the concept of limits to its fullest extent.

E.g. If a function contains an interval (a,b). Where c ∈ (a,b). Then the slope of the tangent at the curve would be f'(c). Where f'(c) is the position of the body at x=c. Or, x=t.

Is this correct?

What type of math is this, is it calculus math?

@Ostronomos

I'm looking up what is ∈

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In math, the symbol ∈ is used to indicate set membership, or that something is an element of a set. It is read as "is in", "belongs to", or "is a member of". For example, the statement "x∈A" means that "x" is an element of the set "A". This means that "x" is one of the objects in the collection of objects in the set "A".

The symbol ∈ looks similar to a stretched-out lowercase Greek letter epsilon. It is sometimes called the "member of" or "belongs to" symbol.

Here are some other set membership symbols:

• ∉: Means "is not in"
  
  
• ⊆: Means containment of sets

My analyzing:
I have a moving body t. Then its position function f, that contains dominate t. If I want to understand this it'll be f(t). So what the number is of t so will be the same number as f. Example t = 3 then f also will = 3. And this will look like t(3) f(3)

How did the greeks fail 2,000 years ago? Yet about 200 years ago they understand more.

What type of math did they use 2,000 years ago? What type of math did they use 200 years ago?

Can you tell me what type of math you are using? Is this calculus?

Can you give me a beginners question so I can begin to learn this type of math?

Body t dominate movement f. How come both t and f has the same numbers? What would happen if they have different numbers?

Added edit

Is algebra the same as calculus? No. Though they are closely related, they both belong to different branches of mathematics. While calculus deals with operations on functions and their derivatives, algebra involves operations on numbers and variables.Oct 23, 2020

Algebra vs calculus | Linear Algebra vs Calculus and more​