MetalheadGautham
AFK
Going by your example lets say after infinite years you want to know their age difference, you do not know their age difference from start, neither do they(forgot), now can you calculate it?
Nope. Which is why I said you can handle infinite values in certain situations where you know their origins and you are able to obtain a finite value using a relation between the two infinite values
Meaning anything divided by infinity is ZERO. But sometimes, there come places in mathematics where infinity gets reduced to a finite value. Here we can solve.
As far you and them are concerned both of them had lived for an eternity and you don't know how 'old' they exactly are, so you can no differentiate them.
When trying to subtract two numbers(coarse example) that had been integrated over an infinite range, you do not know their limiting values, hence you cannot subtract them.
Lemme give you another picture. Take two random infinite numbers. Their difference is indeterminate because we don't know what is the value by which the two differ.
But sometimes you DO know how the numbers originated. This happens in many of the common problems you encounter when making mathematical calculations. In these places, there are well defined procedures to solve the problem.
I'm not trying to say infinity is solvable, so your point holds true. But sometimes problems where you encounter terms tending to infinity there occur situations where you can rearrange stuff so that you don't get infinity anymore.
@MHG : Mathematical fallacy
For dealing with infinity, you need to have a pretty strong visualization to get some vague idea, but at the same time you cannot visualize infinity.
y=e^x is a theoretical formula. Not everything in the world is based on theoretical formula. Earth seems to be "flat" from a lower frame of awareness or consciousness, but "round" from a higher frame of awareness. Similarly, you can visualize y=e^x till it is within limits. On the graph, if "1cm represents 1 km" (i.e visualization), then y=e^x may look like a straight line. If you put x=infinity, then y becomes infinity. You may still see a curve depending upon your frame of reference, but how sure can you be without the use of formula that it is still a curve? Even with the formula..
y=e, when x=1, i.e y!=x
y=e^2 when x=2 i.e y!=x
y=infinty when x=infinty i.e y becomes equal to x now (?) and the formula breaks from its consistency (?).
You can deduce the formula of the graph, i.e reverse, if you are given the graph within limits. But you cannot when infinity comes into the picture. You cannot know if its a square, circle or a line then.
most of your reply is above.
as I said, your statements are correct. I only provided a solution for a small subset of infinity problems where infinity is really not infinity which is the case with many situations!
y -> infinity only means that the variable is "approaching/tends to" infinity. It doesn't mean that it is infinity! Ponder over it and you might become a philosopher. In deep state of meditation (with eyes closed), you may experience that infinite. You cannot know where that blank starts or its depth. Ironically, you will realize that it is also a state of "nothingness" or emptiness! That emptiness may manifest into a thought and that thought into a dream.....well I got carried away