Interesting Number ONE

I discovered that there are two numbers that amaze me. They are ZERO and ONE.

I had posted interesting facts about the number ZERO some time back. You may visit this post to read about ZERO.

How about the number ONE? What's so interesting?

5 x 1 = 5

35656 x 1 = 35656

What does this "1" do for the above 2 math operations ?

It seems like this "1" has no significance.

How about division?

4 /1 = 4

45 / 1 = 45

Again this "1" has no impact on the result!

How about 2¹?

The result is 2. The "1" is transparent!

If your pay is $1000, is the "1" important? You bet !

The number ONE is therefore important when it should be.

Can we write "1" in another way?

1 = log₅5

1 = A⁰

1 = A / A

ONE can be hidden also. TAKE NOTE ! This is where common mistakes are made!

What is the amplitude of y = sin 45⁰?

Some math learners give the answer as ZERO !

The actual answer is the hidden ONE. Not ZERO!

This is because 1 x "anything" gives the original "anything".

How about factorising Y + aY ?

Answer is Y (1 + a).
Where did the "1" comes from?

The question is actually (1)Y + aY, with the "1" hidden besides the first term of X.
(I never expect the "1" to be that shy!).

Now, having shown the facts about ONE, how is this number ONE doing in math?

Powerful and mysterious one, right?
.