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Huh. Most of those make sense to me, but infinity == infinity being true definitely feels like risky business. Algebraic limits is full of even some pretty triv

Huh. Most of those make sense to me, but infinity == infinity being true definitely feels like risky business. Algebraic limits is full of even some pretty trivial scenarios where infinity divided by a lesser-infinity turns out to be a real number— those cases where the two infinities are definitely not equal to each other.

MichaelMoser123 4y ago
Also: in javascript you can divide by zero > 1/0 Infinity But python throws a divide by zero error: >>> 1/0 Traceback (most recent call last): File "<stdin>", line 1, in <module> ZeroDivisionError: division by zero Still you do have infinity and nan in python - because these are part of the floating point spec. >>> float('inf') - float('inf') nan >>> float('inf') == float('inf') True >>> NAN=float('inf') - float('inf') >>> NAN == NAN False However that's not mathematics, it's computers (these are even stranger...) I have my own little programming language - PYX [1] - and i don't allow this madness (even if it is a violation of the floating point spec ;-) pyx > mathconst.Infinity - mathconst.Infinity Error: results in 'not a number' - that's not allowed here #(1) mathconst.Infinity - mathconst.Infinity |....................^ > 1/0 Error: Can't divide by zero #(1) 1/0 |..^ [1] PYX - https://github.com/MoserMichael/jscriptparse https://github.com/MoserMichael/jscriptparse - it's supposed to be an educational programming language, where I am trying to have detailed error messages, my side project.
- pclmulqdq 4y ago
  Dividing by 0 or -0 is a valid floating-point operation because there's an infinity in the number system, and JS uses double precision floating point for all numbers. Python has an integer type and a double type, and division by 0 is disallowed for integers, but okay for doubles.
  - MichaelMoser123 4y ago
    your explanation makes sense, however python doesn't allow division of floating point number by 0 either: >>> type(1.0) <class 'float'> >>> 1.0/0 Traceback (most recent call last): File "<stdin>", line 1, in <module> ZeroDivisionError: float division by zero However numpy lets you do it - it is only a warning >>> import numpy as np >>> >>> np.divide(1.0,0) __main__:1: RuntimeWarning: divide by zero encountered in true_divide inf
    - pclmulqdq 4y ago
      Wow, Python really does hold your hand. >>> 1/0.0 Traceback (most recent call last): File "<stdin>", line 1, in <module> ZeroDivisionError: float division by zero >>> 1.0/0.0 Traceback (most recent call last): File "<stdin>", line 1, in <module> ZeroDivisionError: float division by zero
hunter2_ 4y ago
> those cases where the two infinities are definitely not equal to each other It's been a while since I was doing this in a classroom, but I feel like those things you're thinking are nonuniform infinities could just as well be thought of as entities comprised of infinity and a (perhaps implied) coefficient. Divide out infinity to reveal the coefficient. (And the same for powers/logs, etc.) In this model, infinities are indeed uniform (quite similar to a constant), though they are often augmented in any of infinitely many ways.

MichaelMoser123 4y ago

Also: in javascript you can divide by zero > 1/0 Infinity But python throws a divide by zero error: >>> 1/0 Traceback (most recent call last): File "<stdin>", line 1, in <module> ZeroDivisionError: division by zero Still you do have infinity and nan in python - because these are part of the floating point spec. >>> float('inf') - float('inf') nan >>> float('inf') == float('inf') True >>> NAN=float('inf') - float('inf') >>> NAN == NAN False However that's not mathematics, it's computers (these are even stranger...) I have my own little programming language - PYX [1] - and i don't allow this madness (even if it is a violation of the floating point spec ;-) pyx > mathconst.Infinity - mathconst.Infinity Error: results in 'not a number' - that's not allowed here #(1) mathconst.Infinity - mathconst.Infinity |....................^ > 1/0 Error: Can't divide by zero #(1) 1/0 |..^ [1] PYX - https://github.com/MoserMichael/jscriptparse https://github.com/MoserMichael/jscriptparse - it's supposed to be an educational programming language, where I am trying to have detailed error messages, my side project.

pclmulqdq 4y ago
Dividing by 0 or -0 is a valid floating-point operation because there's an infinity in the number system, and JS uses double precision floating point for all numbers. Python has an integer type and a double type, and division by 0 is disallowed for integers, but okay for doubles.
- MichaelMoser123 4y ago
  your explanation makes sense, however python doesn't allow division of floating point number by 0 either: >>> type(1.0) <class 'float'> >>> 1.0/0 Traceback (most recent call last): File "<stdin>", line 1, in <module> ZeroDivisionError: float division by zero However numpy lets you do it - it is only a warning >>> import numpy as np >>> >>> np.divide(1.0,0) __main__:1: RuntimeWarning: divide by zero encountered in true_divide inf
  - pclmulqdq 4y ago
    Wow, Python really does hold your hand. >>> 1/0.0 Traceback (most recent call last): File "<stdin>", line 1, in <module> ZeroDivisionError: float division by zero >>> 1.0/0.0 Traceback (most recent call last): File "<stdin>", line 1, in <module> ZeroDivisionError: float division by zero

hunter2_ 4y ago

> those cases where the two infinities are definitely not equal to each other It's been a while since I was doing this in a classroom, but I feel like those things you're thinking are nonuniform infinities could just as well be thought of as entities comprised of infinity and a (perhaps implied) coefficient. Divide out infinity to reveal the coefficient. (And the same for powers/logs, etc.) In this model, infinities are indeed uniform (quite similar to a constant), though they are often augmented in any of infinitely many ways.