Building blocks (1st of a riddle series)

Question

"We are the basic building blocks
of something you use everyday.
We constitute them almost all,
being part of them in some way.

We're like a ray in some respect,
in that we begin and not end.
But a ray's continuous and we're not,
of the gaps we're constituent.

In a gap, each can be dismantled
into us, and each of us may recur.
If someone tries to disassemble us,
nothing would occur.

Who are we?"

Answer 1

The factors of this unique rhyme,

describe the numbers which are prime.

We are the basic building blocks of something you use everyday.

Natural numbers greater than one can be written as a product of primes - shown in Euclid.
ngn notes that $1$ is defined as the empty product of $\mathbb{N}$

We constitute them almost all, being part of them in some way.

The natural numbers include $1$ which nowadays is not a included in the primes for convenience of expressing theorems. $0$ is a natural number for e.g. set rather than number theorists - though all use it to express the natural numbers in a base system.

We're like a ray in some respect, in that we begin and not end.

The prime numbers start at 2 and continue indefinitely - again Euclid.
Or for interesting PDF download Edsger Dijkstra

But a ray's continuous and we're not, of the gaps we're constituent.

After 3 there are always gaps between the primes for example the multiples of two.

In a gap, each can be dismantled into us, and each of us may recur.

The gaps between prime numbers are composite and can be written as a product of primes (which may be repeated) e.g. $ 4 = 2^2 , 6 = 2\cdot3, ... $
These gaps are indefinitely large, e.g. the numbers from $n! + 2$ to $n! + n$, but there are an infinite number of bounded gaps, of at most size $246$ - see Prime gaps.

If someone tries to disassemble us, nothing would occur.

A prime cannot be factorised into a product of primes, the only prime which divides it is itself.

Who are we? You are

the prime numbers $2,3,5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, ...$

Answer 2

Are you

The set of whole numbers (0, 1, 2, 3...)?

"We are the basic building blocks
of something you use everyday.

Most people use numbers (and math, which is built from numbers) everyday.

We constitute them almost all,
being part of them in some way.

Almost all numbers (other than irrational numbers) can be represented by division of whole numbers. Negative numbers can't, but whole numbers can still be part of them "in some way," just without the minus sign.

We're like a ray in some respect,
in that we begin and not end.

They start at 0, but continue increasing until positive infinity.

But a ray's continuous and we're not,
of the gaps we're constituent.

But there is no whole number between 1 and 2, or 2 and 3, or any of those gaps.

In a gap, each can be dismantled
into us, and each of us may recur.

Maybe referring to fractions - e.g., 1/3 can be dismantled into a 1 and a 3? 1/3 is also .33333333, where 3 is recurring.

If someone tries to disassemble us,
nothing would occur.

If you disassemble us (subtract? or simply get rid of?) the whole numbers, you'd be left with only negative numbers on the number line, which are nothing.

Answer 3

You are:

Photons (That make up light)

Explanation:

Title

Building blocks of light

We are the basic building blocks
of something you use everyday.
We constitute them almost all,
being part of them in some way.

We use bulbs/CFL's everyday. Light indeed constitutes almost all of our daily activities.

We're like a ray in some respect,
in that we begin and not end.
But a ray's continuous and we're not,
of the gaps we're constituent.

Photons are the proof for particle nature of light disproving its ray/wave nature.

In a gap, each can be dismantled
into us, and each of us may recur.
If someone tries to disassemble us,
nothing would occur.

Gaps can be dismantled into photons, but if we someone tries to disassemble photons. It will lead to complete darkness, stopping the basic need for human survival i.e. nothing would occur. Our ecosystem will collapse.

Answer 4

I'm going to guess at

bricks

Title:

Building blocks of houses

We are the basic building blocks
of something you use everyday.
We constitute them almost all,
being part of them in some way.

We live in houses, therefore we use them everyday. Nearly all houses are brick houses.

We're like a ray in some respect,
in that we begin and not end.
But a ray's continuous and we're not,
of the gaps we're constituent.

Once assembled, the house has no end, as it is a continuous line of bricks. However, bricks are used to fill in gaps in walls.

In a gap, each can be dismantled
into us, and each of us may recur.
If someone tries to disassemble us,
nothing would occur.

Again, bricks are used to fill gaps. Bricks are pretty solid, and trying to disassemble one they will find it impossible.

Who are we?"

Bricks?