If 2d is only length and width, but not depth then can something really exist in 2d?

Question

2d is length and width, not depth. So if I have an object in 2d (0 depth), then it would be non-existent, right? Paper, graphite, etc. have depth even if it is extremely small. Here is my own theory on the 2cnd dimension:The first thing that comes to my mind would be light, but it is made up of waves which have length width and depth. But I thought for a while and realized that color has no depth, but physically exist in our world. Color being how much light is reflected from an object (or how much of one or more types of light waves are absorbed by an object) then, is 2d. So another question I have is, would 2d be measured by length and width, or something like temperature and frequency?

EDIT

I would ask anybody leaving comments to bear in mind that the OP is a potential physicist, at some time in the future and would probably appreciate encouragement. Thanks........ Count_to_10

END EDIT

Answer 1

(...)
'I do not mean to ask you to accept anything without reasonable ground for it. You will soon admit as much as I need from you. You know of course that a mathematical line, a line of thickness nil, has no real existence. They taught you that? Neither has a mathematical plane. These things are mere abstractions.'
'That is all right,' said the Psychologist.
'Nor, having only length, breadth, and thickness, can a cube have a real existence.'
'There I object,' said Filby. 'Of course a solid body may exist. All real things-'
'So most people think. But wait a moment. Can an instantaneous cube exist?'
'Don't follow you,' said Filby.
'Can a cube that does not last for any time at all, have a real existence?' Filby became pensive. 'Clearly,' the Time Traveller proceeded, 'any real body must have extension in four directions: it must have Length, Breadth, Thickness, and - Duration. '
(...)

H. G. Wells, The Time Machine (1895)