what is the value of infinity???and also prove it.
Answers
Step-by-step explanation:
Infinity is not a number, and therefore cannot be defined solely in terms of a number or any combination of numbers (using the elementary operations).
However, before you say “wait a minute!” .. I can define infinity to be one divided by zero, or any number divided by zero, look closely at what that equation says:…. In effect, multiplying both sides of the equation by zero (to remove the division by zero, normally an impermissible operation), you obtain the “nonsensical” (more mildly, counter-intuitive) equation that something finite (one, or whatever number you chose to “illegally” divide by zero) is equal to ZERO multiplied by infinity…. And we know that any (finite) number multiplied by zero is zero, we therefore cannot think of infinity as just an ordinary number! (And consequently, there is something inherently wrong about writing an equation that involves division by zero).
So, something else is needed to allow us to make sense of that equation, and the closely allied question to the one you have asked, “what number lies closest to zero?”.
What is necessary at this point is the concept of a limit, which answers both questions…. Infinity is obtained only by a process of division by a number which is closer and closer to zero, but is never actually zero…. And the number obtained is as close to infinity as we please once the number in the denominator is shrunk sufficiently far.
As we can never reach a number infinitely close to zero, we can never attain a number close enough to infinity to say “we have arrived!”. The equation involving division by zero can then be seen to express a truth that only is attained “in the limit”, or “at” the limit…. Which is conceptually attainable, but never attainable in reality.
What we have actually done by introducing the concept of a limit, then, is to show a subtle (and unifying) inter-relationship between the idea of the incomprehensible large and the equally ideal concept of the vanishingly small.