Fixed MathJax.

Source Link

edit approved Nov 16, 2017 at 23:48

1
2
3

According to constructivism, "it is necessary to find (or "construct") a mathematical object to prove that it exists". There are several formulas to calculate pi$\pi$, such as:

formula for pi (image source)

so I take it pi$\pi$ exists according to constructivism.

According to finitism, which is a form of constructivism, "a mathematical object does not exist unless it can be constructed from natural numbers in a finite number of steps."

Where does that leave irrational numbers, such as pi$\pi$? Do they simply not exist according to finitism? How does one reason about the ratio between a circle's circumference and its diameter, if one is working within a finitistic/ultrafinitistic framework?

According to constructivism, "it is necessary to find (or "construct") a mathematical object to prove that it exists". There are several formulas to calculate pi, such as:

formula for pi (image source)

so I take it pi exists according to constructivism.

According to finitism, which is a form of constructivism, "a mathematical object does not exist unless it can be constructed from natural numbers in a finite number of steps."

Where does that leave irrational numbers, such as pi? Do they simply not exist according to finitism? How does one reason about the ratio between a circle's circumference and its diameter, if one is working within a finitistic/ultrafinitistic framework?

According to constructivism, "it is necessary to find (or "construct") a mathematical object to prove that it exists". There are several formulas to calculate $\pi$, such as:

formula for pi (image source)

so I take it $\pi$ exists according to constructivism.

According to finitism, which is a form of constructivism, "a mathematical object does not exist unless it can be constructed from natural numbers in a finite number of steps."

Where does that leave irrational numbers, such as $\pi$? Do they simply not exist according to finitism? How does one reason about the ratio between a circle's circumference and its diameter, if one is working within a finitistic/ultrafinitistic framework?

Copied image to imgur.com, as it was not being displayed because of the new https rule. Added link to original image source. Deleted unwanted backslash/

Source Link

edit approved Nov 16, 2017 at 23:20

jeq

1.2k
5
16
21

What is the status of irrational numbers within finitism/ultrafinitism?

According to [constructivism](http://en.wikipedia.org/wiki/Constructivism_(mathematics\))constructivism, "it is necessary to find (or "construct") a mathematical object to prove that it exists". There are several formulas to calculate pi, such as:

formula for pi http://mathworld.wolfram.com/images/equations/PiFormulas/NumberedEquation3.gif(image source)

so I take it pi exists according to constructivism.

According to finitism, which is a form of constructivism, "a mathematical object does not exist unless it can be constructed from natural numbers in a finite number of steps."

Where does that leave irrational numbers, such as pipi? Do they simply not exist according to finitism? How does one reason about the ratio between a circle's circumference and its diameter, if one is working within a finitistic/ultrafinitistic framework?

What is the status of irrational numbers within finitism/ultrafinitism?

According to [constructivism](http://en.wikipedia.org/wiki/Constructivism_(mathematics\)), "it is necessary to find (or "construct") a mathematical object to prove that it exists". There are several formulas to calculate pi, such as:

formula for pi http://mathworld.wolfram.com/images/equations/PiFormulas/NumberedEquation3.gif

so I take it pi exists according to constructivism.

According to finitism, which is a form of constructivism, "a mathematical object does not exist unless it can be constructed from natural numbers in a finite number of steps."

Where does that leave irrational numbers, such as pi? Do they simply not exist according to finitism? How does one reason about the ratio between a circle's circumference and its diameter, if one is working within a finitistic/ultrafinitistic framework?

What is the status of irrational numbers within finitism/ultrafinitism?

According to constructivism, "it is necessary to find (or "construct") a mathematical object to prove that it exists". There are several formulas to calculate pi, such as:

formula for pi (image source)

so I take it pi exists according to constructivism.

According to finitism, which is a form of constructivism, "a mathematical object does not exist unless it can be constructed from natural numbers in a finite number of steps."

Where does that leave irrational numbers, such as pi? Do they simply not exist according to finitism? How does one reason about the ratio between a circle's circumference and its diameter, if one is working within a finitistic/ultrafinitistic framework?