- #1
jacket
- 32
- 1
I know ∞ is not really a number. It represents 'greater than every real number'. And for any real number x, we can say
-∞ < x < +∞
Now, my questions are -
(A) how come arithmetic operators interact with ∞ if it is not a number?
(B) what are the results for the expressions below?
(C) and also why we do have results for these if ∞ is not a number?
01. (+∞) + (+∞) =
02. (-∞) + (-∞) =
03. (+∞) + (-∞) =
04. (+∞) - (+∞) =
05. (+∞) - (-∞) =
06. (-∞) - (-∞) =
07. (+∞) * (+∞) =
08. (-∞) * (+∞) =
09. (-∞) * (-∞) =
10. (+∞) / (+∞) =
11. (+∞) / (-∞) =
12. (-∞) / (+∞) =
13. (-∞) / (-∞) =
14. (+∞) + any real number > 0 =
15. (-∞) + any real number > 0 =
16. (+∞) - any real number < 0 =
17. (-∞) - any real number < 0 =
18. (+∞) * (any real number > 0) =
19. (+∞) * (any real number < 0) =
20. (-∞) * (any real number > 0) =
21. (-∞) * (any real number < 0) =
22. (+∞) * 0 =
23. (-∞) * 0 =
24. (+∞) / (any real number > 0) =
25. (+∞) / (any real number < 0) =
26. (-∞) / (any real number > 0) =
27. (-∞) / (any real number < 0) =
28. (+∞) / 0 =
29. (-∞) / 0 =
30. (+∞) ^ (any real positive number except 0, 1) =
31. (+∞) ^ (any real negative number except 0, -1) =
32. (-∞) ^ (any real positive number except 0, 1) =
33. (-∞) ^ (any real negative number except 0, -1) =
34. (+∞) ^ 0 =
35. (+∞) ^ 1 =
36. (+∞) ^ -1 =
37. (-∞) ^ 0 =
38. (-∞) ^ 1 =
39. (-∞) ^ -1 =
40. (+∞) ^ (+∞) =
41. (-∞) ^ (-∞) =
42. (+∞) ^ (-∞) =
43. (-∞) ^ (+∞) =
44. 1 / (+∞) =
45. 0 / (+∞) =
46. 1 / (-∞) =
47. 0 / (-∞) =
48. 0 / 0 =
49. 1 / 0 =
50. 0 / (+∞) =
51. 0 / (-∞) =
52. 1 ^ (+∞) =
53. 1 ^ (-∞) =
54. 0 ^ (+∞) =
55. 0 ^ (-∞) =
I know that is long. But I will very much appreciate your help.
-∞ < x < +∞
Now, my questions are -
(A) how come arithmetic operators interact with ∞ if it is not a number?
(B) what are the results for the expressions below?
(C) and also why we do have results for these if ∞ is not a number?
01. (+∞) + (+∞) =
02. (-∞) + (-∞) =
03. (+∞) + (-∞) =
04. (+∞) - (+∞) =
05. (+∞) - (-∞) =
06. (-∞) - (-∞) =
07. (+∞) * (+∞) =
08. (-∞) * (+∞) =
09. (-∞) * (-∞) =
10. (+∞) / (+∞) =
11. (+∞) / (-∞) =
12. (-∞) / (+∞) =
13. (-∞) / (-∞) =
14. (+∞) + any real number > 0 =
15. (-∞) + any real number > 0 =
16. (+∞) - any real number < 0 =
17. (-∞) - any real number < 0 =
18. (+∞) * (any real number > 0) =
19. (+∞) * (any real number < 0) =
20. (-∞) * (any real number > 0) =
21. (-∞) * (any real number < 0) =
22. (+∞) * 0 =
23. (-∞) * 0 =
24. (+∞) / (any real number > 0) =
25. (+∞) / (any real number < 0) =
26. (-∞) / (any real number > 0) =
27. (-∞) / (any real number < 0) =
28. (+∞) / 0 =
29. (-∞) / 0 =
30. (+∞) ^ (any real positive number except 0, 1) =
31. (+∞) ^ (any real negative number except 0, -1) =
32. (-∞) ^ (any real positive number except 0, 1) =
33. (-∞) ^ (any real negative number except 0, -1) =
34. (+∞) ^ 0 =
35. (+∞) ^ 1 =
36. (+∞) ^ -1 =
37. (-∞) ^ 0 =
38. (-∞) ^ 1 =
39. (-∞) ^ -1 =
40. (+∞) ^ (+∞) =
41. (-∞) ^ (-∞) =
42. (+∞) ^ (-∞) =
43. (-∞) ^ (+∞) =
44. 1 / (+∞) =
45. 0 / (+∞) =
46. 1 / (-∞) =
47. 0 / (-∞) =
48. 0 / 0 =
49. 1 / 0 =
50. 0 / (+∞) =
51. 0 / (-∞) =
52. 1 ^ (+∞) =
53. 1 ^ (-∞) =
54. 0 ^ (+∞) =
55. 0 ^ (-∞) =
I know that is long. But I will very much appreciate your help.