~~~無限的問題~~~

2007-10-09 12:51 am
Can you tell me the following statements are true or not

1.無限>無限 - 1
2.assume that x+y =無限 and x=y so 無限/2 is equal to x or y
3. In number line , the mid point of 無限 and - 無限 is 0
4.無限 is an irrational number , the deimal place of pi (3.14.....) is 無限 so pi is an irrational number
5.can i use 無限 to describe the distance of the space ?
6. 無限km = 無限m

SP answers and explanations please ! thanks

回答 (2)

2007-10-09 1:17 am
✔ 最佳答案
All of your assumptions are not correct, infinity cannot not be calcalated, as
1&2)
x>x-1, but infinity=infinity-1, and same for adding and substrction except infinity-infinity, that is unknown, unless you stated others condition, like
x trends to infinity, x-x/2=x/2, x/2 trends to infinity.
3)
The mid point is (x+y)/2, even x and y is +/- infinity. eg x trends to infinity, then the mid point of x and -x/2 is [x+(-x/2)]/2=x/4, it is infinity.
4)
You mixed up the idea of infintity, pi is not infinity even it is a irrational number.
since 4>pi>2, pi is a fixed value, there is nothing greater than +infinty or small than -infinity, pi is a number.
5)
No, there is an estimated size, the sphere of our universe is about 150,000,000,000 light years in radius. It is a very very large number but not infinity. The distance between Earth and moon is 380,000 km, ~1.267 light second. 1 ly (light year) means the distance travelled by light in 1 year, 1 ls (light second) is the distance light travel in 1 s.
6) No.
2007-10-21 1:25 am
如果可以把無限這個概念和數字分開會更好。


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