## UnkleRhaukus 3 years ago $\infty\times0=$

1. Fox375

0!!!!

2. UnkleRhaukus

@lgbasallote

0

4. satellite73

definitely $$\pi$$

5. Fox375

@satellite73 IKR

6. UnkleRhaukus

7. satellite73

oh wait, i am wrong it is $$e^2$$ sorry

8. lgbasallote

you can rewrite $\infty \times 0$ as $\infty \times \frac 1\infty$ right? then it becomes l'hospital...

9. lgbasallote

assuming of course these are functions...

10. UnkleRhaukus

there is another way

11. lgbasallote

really? hmm

12. lgbasallote

change infinity to 1/0 to make it 0/0?

13. lgbasallote

either way...it's indeterminate....

14. satellite73

if this is a serious question, presumably it is about limits, i.e. if $$\lim_{x\to\infty}f(x)=\infty$$ and $$\lim_{x\to \infty}g(x)=0$$ then what is $\lim_{x\to \infty}f(x)g(x)$ the answer is it could be anything, it depends on $$f$$ and $$g$$ the form is not determined

15. CliffSedge

$\large a \times b = c$ $\large a=\frac{c}{b}$ $\large b=\frac{c}{a}$ Let a = ∞, b=0 $\large ∞=\frac{c}{0}$ $\large 0=\frac{c}{∞}$ But c/0 is undefined and so is c/∞, right? What if c were positive? What if c were negative?

16. satellite73

so it could be $$\pi$$ or it could be $$e^2$$ or it could be anything

17. lgbasallote

an interesting question though is... $\frac 1 \infty = 0$ therefore... $0 \times \infty = 1$ that should be right?

18. lgbasallote

just expressing how weird math is

19. satellite73

not at all

20. satellite73

infinity is not a number, and so $$\frac{1}{\infty}$$ is not a number either

21. CliffSedge

Agree with @satellite73 To say that 1/∞ = 0, you have to take the limit of 1/x as x-->∞ and then 0 × (x is really really big) still equals 0.

22. UnkleRhaukus

|dw:1349968485543:dw|

23. lgbasallote

math is still weird....

24. CliffSedge

(I'm going to have to go get coffee, then come back for this. Unkle is about to get all Twilight Zone on us, I can feel it.)

25. satellite73

you are making short cut statements about limits namely if $\lim_{x\to\infty}f(x)=\infty$ then $\lim_{x\to \infty}\frac{1}{f(x)}=0$

26. lgbasallote

i never really understood the function of limits...

27. lgbasallote

math is too ambiguous for me

28. satellite73

$$\infty$$ is not a number $$\infty\times 0$$ is not a number $\frac{5}{\infty}$ is not a number

29. CliffSedge

(aside: Anybody hear the full treatment of 'Hilbert's Hotel?')

30. CliffSedge

Is the slope of the vertical line +∞ or -∞ @UnkleRhaukus ?

31. UnkleRhaukus

i dont know what 'Hilbert's Hotel?' is

32. CliffSedge

Check it out some time. David Deutsch gives a good telling of it in his book, 'The Beginning of Infinity.' (Fantastic book on the philosophy of science; I recommend it to everyone.)

33. UnkleRhaukus

the product of the slopes of perpendicular lines is

34. CliffSedge

Yes, but what is the slope of the vertical line?

35. UnkleRhaukus

$\pm\infty$

36. helder_edwin

this might help

37. JamesWolf

infinity is stupid. $\infty + 1 = \infty$ $1 = \infty - \infty = 0$

38. UnkleRhaukus

$\infty\times 0=-1$

39. JamesWolf

all the even numbers = $\infty$ which is smaller than all the numbers = $\infty$ so $\infty < \infty$

40. CliffSedge

$\large 2 \times ∞ \times 0 = -2?$

41. CliffSedge

@JamesWolf there are different cardinalities of infinity. Research "Aleph Numbers" for more info. The infinity of integers is less than the infinity of real numbers, etc.

42. Jemurray3

The bastardization of mathematics that has taken place in this thread is like salt rubbed into a fresh wound of my soul. Is there a legitimate question, or are you guys just playing around? :)

43. 03453660

this is definitely an undefined case because any number multiplied with zero become zero and any number multiplied with infinity become infinity that's why both of these cases are possible here therefore we cannot consider one these case separately. thus this is an undefined case.

44. CliffSedge

@Jemurray3 I don't think there's anything serious going on. Unkle came up with a cute link to slopes of parallel lines, but made the error in saying that vertical lines have a slope, m=∞, which, of course, is false.

45. Coolsector

if the question is something like lim x->inf of 0*x then it is 0 otherwise we should be more specific about the problem i guess