Reals

Why do so many languages include the type of "real" numbers if real numbers are physically impossible to represent in any computer? There are no and will never be realnums in any computer, stop deluding yourselves.

hax my anus

WTF?

Of course you can represent them in a computer. Even irrational ones. You represent them symbolically

e.g. the Lisp forms

'(sqrt 2)
pi

Represent irrational, real numbers.

Try using a CAS e.g. Maxima or Mathematica and learning how they work.

>>3
Try representing pi or e in a computer.
And in many programming languages a realnum is just a misnomer for a limited-precision floating-point number. And that is just lunacy and delusion. 64 bits are not a "real number".

>>4
'e
'pi

There, I represented both.


In[33]:= 2 * Pi
Out[33]= 2 \[Pi]

In[34]:= 2 * Pi * E
Out[34]= 2 E \[Pi]

In[35]:= Sqrt[2 * E * Pi]
Out[35]= Sqrt[2 E \[Pi]]

In[36]:= N[Sqrt[2 E \[Pi]], 50]
Out[36]= 4.1327313541224929384693918842998526494455219169913

In[37]:= N[Sqrt[2 * E * Pi], 100]

Out[37]= 4.\
1327313541224929384693918842998526494455219169913084515566512537979579\
28513417032362520362455466283

Do you understand yet?

In case you don't understand I'll spell it out for you:

Sqrt[2 * E * Pi]

is a computer representation, as an M-expression of a real number. The exact encoding of the M-expression is not really important, but ultimately it is encoded in binary.

The function N evaluates the precise "lossless" (if you will) computer representation of a real number into a lossy decimal representation to some specified amount of digits.

Nevertheless, it is evident that a computer can easily represent, manipulate and compute with, a real number.

>>7
An M-expression is no more a real number than the Greek letter pi is the number pi. It is a symbol, not a number.
Even computation of a real number to arbitrary precision does not mean the real number itself is ever represented in computer memory.
There is no precise "lossless", as you call it, computer representation of an arbitrary real number as it would overfill any memory. You are lying.
Thus saying that any programming language has a "real number" type is misleading, arrogant and delusional. Computers have floating-point numbers, sure, but not real numbers.

>>1
Rational numbers can easily be represented in a computer program by defining them as the quotient of two integers. Irrational numbers must be, just like IRL, represented by an approximation or a symbol.

>>9
But in programming languages that have a realnum type it is not a type of symbols or even rational numbers, but simply floating-point numbers.

>>10
those are shit languages

>>11
I'm sorry you can't appreciate REAL programming languages.

The ``goo nuff'' ``real'' numbers in most programming languages can't even represent 0.1 exactly, let alone real numbers.

>>13
0.1
0.0001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100

>>8
Yes, it's not a real number. It's a representation of a real number. Like a machine word can be a representation of integers (a subset of real numbers) or certain decimals (floating point numbers).

A physical entity can never be a number, it can only represent it.

A physical entity can never be a number, it can only represent it.
I actually have a seven in my pocket right now.

>>16
I have a fourteen in my crotch, if you know what i mean

>>3
Still nowhere close to 'real numbers'
The best you can do is rational numbers + extension fields.