Infinity

[PeterSeeksKnowledge]

Infinity plus Anything, call it Infinity + 1 = Infinity

but

Infinity - 1 = less than Infinity.

Is that possible ?

[MigL]

It isn't.
Infinity is not a number.

[PeterSeeksKnowledge]

If Infinity is a Concept and not a number, can you subtract from infinity but not augment it ?

[Phi for All]

1 hour ago, PeterSeeksKnowledge said:

If Infinity is a Concept and not a number, can you subtract from infinity but not augment it ?

By definition, it doesn't behave like a number, so treating it like one causes problems. 

[studiot]

5 hours ago, PeterSeeksKnowledge said:

If Infinity is a Concept and not a number, can you subtract from infinity but not augment it ?

Somewhat depends upon what you mean by a Concept.

Some would say that all numbers are concepts.

It also depends what you mean by a number.

Any number is of no use on its own.  They are all part of some system of numbers or another.

We distinguish many different number systems.

There is no number system that contains every individual number.

When others are telling you that infinity is not a number, what they mean is that infinity is not a 'real' number, or a number in one of the many simpler systems of numbers.

If you would like to indicate where you want to go with this and also give us some idea of your level of mathematical knowledge we can give you are more detailed answer.

[Eise]

15 hours ago, PeterSeeksKnowledge said:

Infinity - 1 = less than Infinity.

No, it isn't. If a number is less than infinity, than it is finite. If you add 1 again, then you still get a finite number. That is a contradiction, so infinity -1 is still infinity.

The warnings you got that 'infinity' does not behave like any other number are perfectly valid: it is not just 'a big number'.

[PeterSeeksKnowledge]

In some limit questions in Calculus, you can exchange a letter for infinity, to make it work.

So, where or why is that justified ?

[studiot]

Peter, if you don't tell us more we can't help you properly.

I gather that English is not your first language, but the more you use it the better and easier it will become.

Letters are symbols and so is infinity, although it is not a letter of any alphabet it comes from ancient Greek.

In mathematics limits are not part of Calculus, although they are often taught just before calculus.

The letters you refer to in the limit expressions are called dummy indices, which means they stand for integers and that you can use any letter, although, l,m,n i,j,k are the most common.

Infinity itself does not correspond to or replace any integer, and only appears at the end of the limit arrow.

This should be read that n 'tends to infinity'  whcih means the process of getting larger larger for ever, but never actually becoming infinity so you don't replace n by infinity.