singleton part and element part in abstract algebra

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If I say

Let P denote the partition of

{0,1,...,99} into 100 singleton parts

and Q denote the partition of {0,1,...,99} into one 100-element part,

Is it correct if I write it as below?

P = { [1],[2],[3],...,[99] }

Q = { [1,2,3,...,99] }

I thought singleton was a set with single element but I am not sure if this is correct or not.

If anyone could help it would be great

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The usual set-theoretic notation in math would be:

$$P = \{ \{0\},\{1\},\dots,\{99\}\}$$

$$Q = \{\{0,1,\dots,99\}\}$$

(You left out the $0$s.)