(Let’s just say that 1g = 9.8 m/s^2 instead. That is equal to 9.8 newtons of force per square kilogram. )
You drop a 1000kg object from 1km high. If it were to fall at a steady rate of 9.8 meters per second, how much force will it undergo when it hits the ground?
Well, Infinity, subtracted by itself, should be zero.
Because even though it is unlimited, no further numbers exist.
So even though Infinity + 5 = Infinity, Infinity = Infinity, never something greater, because nothing greater exists. So just treat Infinity like a number.
So Infinity - Infinity = 0.
If it is true, Infinity - Infinity - Infinity = -Infinity, because 0 - Infinity = -Infinity.
Infinity is only a symbol, mainly used in limits of a sequence. Its meaning is “this sequence, while composed of finite numbers, is approaching infinity, which means the generic term of this sequence will become greater than any number”, and by generic term i mean every term of the sequence from some point onward.
Example: 5,4,10,9,15,14,20… is a sequence of numbers, and if it goes on like this (adding 6, then subtracting 1) it is approaching infinity. For example, it will be bigger than 1000 from the 401st number on, it will be greater than 1000000 from the 400001st number on, etc.
Precisely. In other words, the infinity symbol represents growth without limit.
AAAARGH! Never, ever, ever think that mathematics are defined by opinion. Mathematics is the most pure field of science existing, and does not depend on opinion at all. Tosxychors gives a nice explanation what infinity “represents” (it’s not a number) in his post above.
[size=59]And a number x € C subtracted by itself is 0, not 1.[/size]
Ohwell let’s try and spice thing up a little:
1 . How many positive divisors does the number 543*2 = 5! have?
2 . Paul takes the number 3, erases it and writes 9, then erases it and writes 81, and so on, each time writing the square of the previous number, another 2006 times. What will be the units’ digit of the last number?
3 . In how many ways you can order the letters L A P I S so that the first and the last letters are wovels?
Have fun ^^
Any solution is better accompanied by a demonstration. I’ll put it myself for this one:
The series starts with 3, 9, 81, 6561, 43046721… But the next number’s units digit is only influenced by the units digit of the last number, as any other calculus would work torwards the bigger digits. IE. 8181= 11 + 801 + 180 + 8080= 1 + 80 + 80 + 6400 = 6461. And since 11 = 1, the lastr digit will always be 1 from that moment on.
III: The first letter we can choose in two ways. The second we can choose in three ways, the third in two ways, the fourth in one way and the fifth in one way. The answer is 23211 = 12.